TSTP Solution File: SCT164+1 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SCT164+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 14:10:20 EDT 2023
% Result : Theorem 0.94s 1.33s
% Output : CNFRefutation 1.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT164+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.16/0.34 % Computer : n014.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Thu Aug 24 16:23:48 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.19/0.55 start to proof:theBenchmark
% 0.94/1.28 %-------------------------------------------
% 0.94/1.28 % File :CSE---1.6
% 0.94/1.28 % Problem :theBenchmark
% 0.94/1.28 % Transform :cnf
% 0.94/1.28 % Format :tptp:raw
% 0.94/1.28 % Command :java -jar mcs_scs.jar %d %s
% 0.94/1.28
% 0.94/1.28 % Result :Theorem 0.280000s
% 0.94/1.28 % Output :CNFRefutation 0.280000s
% 0.94/1.28 %-------------------------------------------
% 0.94/1.28 %------------------------------------------------------------------------------
% 0.94/1.28 % File : SCT164+1 : TPTP v8.1.2. Released v5.2.0.
% 0.94/1.28 % Domain : Social Choice Theory
% 0.94/1.28 % Problem : Arrow's Impossibility Theorem 433644, 500 axioms selected
% 0.94/1.28 % Version : Especial.
% 0.94/1.28 % English :
% 0.94/1.28
% 0.94/1.28 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.94/1.28 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.94/1.28 % Source : [Bla11]
% 0.94/1.28 % Names : arrow_433644.500.p [Bla11]
% 0.94/1.28
% 0.94/1.28 % Status : ContradictoryAxioms
% 0.94/1.28 % Rating : 0.53 v8.1.0, 0.56 v7.4.0, 0.60 v7.3.0, 0.55 v7.1.0, 0.61 v7.0.0, 0.60 v6.4.0, 0.54 v6.2.0, 0.64 v6.1.0, 0.77 v6.0.0, 0.70 v5.5.0, 0.81 v5.4.0, 0.79 v5.3.0, 0.81 v5.2.0
% 0.94/1.28 % Syntax : Number of formulae : 533 ( 120 unt; 0 def)
% 0.94/1.28 % Number of atoms : 1402 ( 328 equ)
% 0.94/1.28 % Maximal formula atoms : 12 ( 2 avg)
% 0.94/1.28 % Number of connectives : 1020 ( 151 ~; 27 |; 49 &)
% 0.94/1.28 % ( 128 <=>; 665 =>; 0 <=; 0 <~>)
% 0.94/1.28 % Maximal formula depth : 16 ( 6 avg)
% 0.94/1.28 % Maximal term depth : 16 ( 2 avg)
% 0.94/1.28 % Number of predicates : 37 ( 36 usr; 0 prp; 1-6 aty)
% 0.94/1.28 % Number of functors : 62 ( 62 usr; 24 con; 0-6 aty)
% 0.94/1.28 % Number of variables : 1550 (1538 !; 12 ?)
% 0.94/1.28 % SPC : FOF_CAX_RFO_SEQ
% 0.94/1.29
% 0.94/1.29 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.94/1.29 % 2011-03-01 11:29:56
% 0.94/1.29 % : Renamed from SWW166+1
% 0.94/1.29 %------------------------------------------------------------------------------
% 0.94/1.29 %----Relevant facts (491)
% 0.94/1.29 fof(fact_ext,axiom,
% 0.94/1.29 ! [V_g_2,V_f_2] :
% 0.94/1.29 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 0.94/1.29 => V_f_2 = V_g_2 ) ).
% 0.94/1.29
% 0.94/1.29 fof(fact_assms_I3_J,axiom,
% 0.94/1.29 c_Arrow__Order__Mirabelle_OIIA(v_F) ).
% 0.94/1.29
% 0.94/1.29 fof(fact_u,axiom,
% 0.94/1.29 c_Arrow__Order__Mirabelle_Ounanimity(v_F) ).
% 0.94/1.29
% 0.94/1.29 fof(fact__096c_A_126_061_Ad_096,axiom,
% 0.94/1.29 v_c____ != v_d____ ).
% 0.94/1.29
% 0.94/1.29 fof(fact__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J_A_061_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_096,axiom,
% 0.94/1.29 ! [B_i] :
% 0.94/1.29 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,B_i)))
% 0.94/1.29 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____))
% 0.94/1.29 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,B_i)),v_e____))) )
% 0.94/1.29 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,B_i)),v_n____))
% 0.94/1.29 => ( ( hAPP(v_h____,B_i) = v_n____
% 0.94/1.29 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,B_i)),v_c____),v_e____))) )
% 0.94/1.29 & ( hAPP(v_h____,B_i) != v_n____
% 0.94/1.29 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,B_i)),v_e____))) ) ) ) ) ) ).
% 0.94/1.29
% 0.94/1.29 fof(fact__096ALL_AP_058Prof_O_AALL_AP_H_058Prof_O_AALL_Aa_Ab_O_A_IALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_J_J_A_N_N_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_J_096,axiom,
% 0.94/1.29 ! [B_x] :
% 0.94/1.29 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf))
% 0.94/1.29 => ! [B_xa] :
% 0.94/1.29 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_xa),c_Arrow__Order__Mirabelle_OProf))
% 0.94/1.29 => ! [B_a,B_b] :
% 0.94/1.29 ( ! [B_i] :
% 0.94/1.29 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,B_i)))
% 0.94/1.29 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_xa,B_i))) )
% 0.94/1.29 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(v_F,B_x)))
% 0.94/1.29 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(v_F,B_xa))) ) ) ) ) ).
% 0.94/1.29
% 0.94/1.29 fof(fact_in__mkbot,axiom,
% 0.94/1.29 ! [V_z_2,V_L_2,V_y_2,V_x_2] :
% 0.94/1.29 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,V_L_2),V_z_2)))
% 0.94/1.29 <=> ( V_y_2 != V_z_2
% 0.94/1.29 & ( V_x_2 = V_z_2
% 0.94/1.29 => V_x_2 != V_y_2 )
% 0.94/1.29 & ( V_x_2 != V_z_2
% 0.94/1.29 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2)) ) ) ) ).
% 0.94/1.29
% 0.94/1.29 fof(fact_in__mktop,axiom,
% 0.94/1.29 ! [V_z_2,V_L_2,V_y_2,V_x_2] :
% 0.94/1.29 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,V_L_2),V_z_2)))
% 0.94/1.29 <=> ( V_x_2 != V_z_2
% 0.94/1.29 & ( V_y_2 = V_z_2
% 0.94/1.29 => V_x_2 != V_y_2 )
% 0.94/1.29 & ( V_y_2 != V_z_2
% 0.94/1.29 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2)) ) ) ) ).
% 0.94/1.29
% 0.94/1.29 fof(fact__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_096,axiom,
% 0.94/1.29 hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,hAPP(c_Hilbert__Choice_Oinv__into(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),v_h____),v_n____)))) ).
% 0.94/1.29
% 0.94/1.29 fof(fact__096P_A_058_AProf_096,axiom,
% 0.94/1.29 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P____),c_Arrow__Order__Mirabelle_OProf)) ).
% 0.94/1.29
% 0.94/1.29 fof(fact__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_058_AProf_096,axiom,
% 0.94/1.29 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))),c_Arrow__Order__Mirabelle_OProf)) ).
% 0.94/1.29
% 0.94/1.29 fof(fact_equalityCE,axiom,
% 0.94/1.29 ! [V_ca_2,T_a,V_B_2,V_A_2] :
% 0.94/1.29 ( V_A_2 = V_B_2
% 0.94/1.29 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 0.94/1.29 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) )
% 0.94/1.29 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 0.94/1.29 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ) ).
% 0.94/1.29
% 0.94/1.29 fof(fact_pred__equals__eq2,axiom,
% 0.94/1.29 ! [V_S_2,V_R_2,T_b,T_a] :
% 0.94/1.29 ( hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a,c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a,c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b,c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a,c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a,c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b,c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)
% 0.94/1.29 <=> V_R_2 = V_S_2 ) ).
% 0.94/1.29
% 0.94/1.29 fof(fact_in__rel__def,axiom,
% 0.94/1.29 ! [V_y_2,V_x_2,V_R_2,T_b,T_a] :
% 0.94/1.29 ( c_FunDef_Oin__rel(T_a,T_b,V_R_2,V_x_2,V_y_2)
% 0.94/1.29 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_R_2)) ) ).
% 0.94/1.29
% 0.94/1.29 fof(fact_same__fstI,axiom,
% 0.94/1.29 ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_Pa_2] :
% 0.94/1.29 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 0.94/1.29 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2)))
% 0.94/1.29 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_a,T_b,V_Pa_2,V_R_2))) ) ) ).
% 0.94/1.29
% 0.94/1.29 fof(fact_pred__equals__eq,axiom,
% 0.94/1.29 ! [V_S_2,V_R_2,T_a] :
% 0.94/1.29 ( hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2) = hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)
% 0.94/1.29 <=> V_R_2 = V_S_2 ) ).
% 0.94/1.29
% 0.94/1.29 fof(fact_in__measure,axiom,
% 0.94/1.29 ! [V_f_2,V_y_2,V_x_2,T_a] :
% 0.94/1.29 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omeasure(T_a,V_f_2)))
% 0.94/1.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ).
% 0.94/1.29
% 0.94/1.29 fof(fact_Nitpick_Orefl_H__def,axiom,
% 0.94/1.29 ! [V_r_2,T_a] :
% 0.94/1.29 ( c_Nitpick_Orefl_H(T_a,V_r_2)
% 0.94/1.29 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x)),V_r_2)) ) ).
% 0.94/1.29
% 0.94/1.29 fof(fact_mlex__less,axiom,
% 0.94/1.29 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] :
% 0.94/1.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 0.94/1.29 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))) ) ).
% 0.94/1.29
% 0.94/1.29 fof(fact_n_I1_J,axiom,
% 0.94/1.29 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),v_n____),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))) ).
% 0.94/1.29
% 0.94/1.29 fof(fact_top1I,axiom,
% 0.94/1.29 ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ).
% 0.94/1.29
% 0.94/1.29 fof(fact_UNIV__I,axiom,
% 0.94/1.29 ! [V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ).
% 0.94/1.29
% 0.94/1.29 fof(fact_injh,axiom,
% 0.94/1.29 c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) ).
% 0.94/1.29
% 0.94/1.29 fof(fact_eq__mem__trans,axiom,
% 0.94/1.29 ! [V_A_2,T_a,V_ba_2,V_aa_2] :
% 0.94/1.29 ( V_aa_2 = V_ba_2
% 0.94/1.29 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),V_A_2))
% 0.94/1.29 => hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ) ).
% 0.94/1.29
% 0.94/1.29 fof(fact_eqelem__imp__iff,axiom,
% 0.94/1.29 ! [V_A_2,T_a,V_y_2,V_x_2] :
% 0.94/1.29 ( V_x_2 = V_y_2
% 0.94/1.29 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 0.94/1.29 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ).
% 0.94/1.29
% 0.94/1.29 fof(fact_eqset__imp__iff,axiom,
% 0.94/1.29 ! [V_x_2,T_a,V_B_2,V_A_2] :
% 0.94/1.29 ( V_A_2 = V_B_2
% 0.94/1.29 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 0.94/1.29 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 0.94/1.29
% 0.94/1.29 fof(fact_eq__mem,axiom,
% 0.94/1.29 ! [V_y_2,V_x_2,T_a] :
% 0.94/1.29 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2)))
% 0.94/1.29 <=> V_x_2 = V_y_2 ) ).
% 0.94/1.29
% 0.94/1.29 fof(fact_mem__def,axiom,
% 0.94/1.29 ! [V_A_2,V_x_2,T_a] :
% 0.94/1.29 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 0.94/1.29 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 0.94/1.29
% 0.94/1.29 fof(fact__C3_C,axiom,
% 0.94/1.29 ! [V_P_H_2,V_Pa_2,V_ba_2,V_aa_2] :
% 0.94/1.29 ( V_aa_2 != V_ba_2
% 0.94/1.29 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf))
% 0.94/1.29 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_H_2),c_Arrow__Order__Mirabelle_OProf))
% 0.94/1.29 => ( ! [B_i] :
% 0.94/1.29 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i)))
% 0.94/1.29 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_aa_2)),hAPP(V_P_H_2,B_i))) )
% 0.94/1.29 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2)))
% 0.94/1.29 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_aa_2)),hAPP(v_F,V_P_H_2))) ) ) ) ) ) ).
% 0.94/1.29
% 0.94/1.29 fof(fact_pairwise__neutrality,axiom,
% 0.94/1.29 ! [V_P_H_2,V_Pa_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2] :
% 0.94/1.29 ( V_aa_2 != V_ba_2
% 0.94/1.29 => ( V_a_H_2 != V_b_H_2
% 0.94/1.29 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf))
% 0.94/1.29 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_H_2),c_Arrow__Order__Mirabelle_OProf))
% 0.94/1.29 => ( ! [B_i] :
% 0.94/1.29 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i)))
% 0.94/1.29 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(V_P_H_2,B_i))) )
% 0.94/1.29 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2)))
% 0.94/1.29 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(v_F,V_P_H_2))) ) ) ) ) ) ) ).
% 0.94/1.29
% 0.94/1.29 fof(fact__C4_C,axiom,
% 0.94/1.29 ! [V_P_H_2,V_Pa_2,V_ca_2,V_ba_2,V_aa_2] :
% 0.94/1.29 ( V_aa_2 != V_ba_2
% 0.94/1.29 => ( V_ba_2 != V_ca_2
% 0.94/1.29 => ( V_aa_2 != V_ca_2
% 0.94/1.29 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf))
% 0.94/1.29 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_H_2),c_Arrow__Order__Mirabelle_OProf))
% 0.94/1.29 => ( ! [B_i] :
% 0.94/1.29 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i)))
% 0.94/1.29 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_ca_2)),hAPP(V_P_H_2,B_i))) )
% 0.94/1.29 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2)))
% 0.94/1.29 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_ca_2)),hAPP(v_F,V_P_H_2))) ) ) ) ) ) ) ) ).
% 0.94/1.29
% 0.94/1.29 fof(fact__C1_C,axiom,
% 0.94/1.29 ! [V_P_H_2,V_Pa_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2] :
% 0.94/1.30 ( V_aa_2 != V_ba_2
% 0.94/1.30 => ( V_a_H_2 != V_b_H_2
% 0.94/1.30 => ( V_aa_2 != V_b_H_2
% 0.94/1.30 => ( V_ba_2 != V_a_H_2
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf))
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_H_2),c_Arrow__Order__Mirabelle_OProf))
% 0.94/1.30 => ( ! [B_i] :
% 0.94/1.30 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i)))
% 0.94/1.30 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(V_P_H_2,B_i))) )
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2)))
% 0.94/1.30 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(v_F,V_P_H_2))) ) ) ) ) ) ) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact__C2_C,axiom,
% 0.94/1.30 ! [V_P_H_2,V_Pa_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2] :
% 0.94/1.30 ( V_aa_2 != V_ba_2
% 0.94/1.30 => ( V_a_H_2 != V_b_H_2
% 0.94/1.30 => ( V_aa_2 != V_b_H_2
% 0.94/1.30 => ( V_ba_2 != V_a_H_2
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Pa_2),c_Arrow__Order__Mirabelle_OProf))
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_P_H_2),c_Arrow__Order__Mirabelle_OProf))
% 0.94/1.30 => ( ! [B_i] :
% 0.94/1.30 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(V_Pa_2,B_i)))
% 0.94/1.30 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(V_P_H_2,B_i))) )
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),hAPP(v_F,V_Pa_2)))
% 0.94/1.30 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_a_H_2),V_b_H_2)),hAPP(v_F,V_P_H_2))) ) ) ) ) ) ) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_in__lex__prod,axiom,
% 0.94/1.30 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_ba_2,V_aa_2,T_b,T_a] :
% 0.94/1.30 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_a,T_b),tc_prod(T_a,T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_a,T_b),tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_aa_2),V_ba_2)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_a,T_b,V_r_2,V_s_2)))
% 0.94/1.30 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_aa_2),V_a_H_2)),V_r_2))
% 0.94/1.30 | ( V_aa_2 = V_a_H_2
% 0.94/1.30 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_b_H_2)),V_s_2)) ) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_top__apply,axiom,
% 0.94/1.30 ! [V_x_2,T_b,T_a] :
% 0.94/1.30 ( class_Orderings_Otop(T_a)
% 0.94/1.30 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_IIA__def,axiom,
% 0.94/1.30 ! [V_Fa_2] :
% 0.94/1.30 ( c_Arrow__Order__Mirabelle_OIIA(V_Fa_2)
% 0.94/1.30 <=> ! [B_x] :
% 0.94/1.30 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf))
% 0.94/1.30 => ! [B_xa] :
% 0.94/1.30 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_xa),c_Arrow__Order__Mirabelle_OProf))
% 0.94/1.30 => ! [B_a,B_b] :
% 0.94/1.30 ( ! [B_i] :
% 0.94/1.30 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,B_i)))
% 0.94/1.30 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_xa,B_i))) )
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x)))
% 0.94/1.30 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_xa))) ) ) ) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_unanimity__def,axiom,
% 0.94/1.30 ! [V_Fa_2] :
% 0.94/1.30 ( c_Arrow__Order__Mirabelle_Ounanimity(V_Fa_2)
% 0.94/1.30 <=> ! [B_x] :
% 0.94/1.30 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf))
% 0.94/1.30 => ! [B_a,B_b] :
% 0.94/1.30 ( ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,B_i)))
% 0.94/1.30 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x))) ) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_iso__tuple__UNIV__I,axiom,
% 0.94/1.30 ! [V_x_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_assms_I1_J,axiom,
% 0.94/1.30 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) ).
% 0.94/1.30
% 0.94/1.30 fof(fact__096Lba_A_058_ALin_096,axiom,
% 0.94/1.30 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)) ).
% 0.94/1.30
% 0.94/1.30 fof(fact__096Lab_A_058_ALin_096,axiom,
% 0.94/1.30 hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_Lab____),c_Arrow__Order__Mirabelle_OLin)) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_above__Lin,axiom,
% 0.94/1.30 ! [V_L_2,V_y_2,V_x_2] :
% 0.94/1.30 ( V_x_2 != V_y_2
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
% 0.94/1.30 => hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,V_L_2),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_OLin)) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_mkbot__Lin,axiom,
% 0.94/1.30 ! [V_x_2,V_L_2] :
% 0.94/1.30 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
% 0.94/1.30 => hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,V_L_2),V_x_2)),c_Arrow__Order__Mirabelle_OLin)) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_mktop__Lin,axiom,
% 0.94/1.30 ! [V_x_2,V_L_2] :
% 0.94/1.30 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
% 0.94/1.30 => hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,V_L_2),V_x_2)),c_Arrow__Order__Mirabelle_OLin)) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_notin__Lin__iff,axiom,
% 0.94/1.30 ! [V_y_2,V_x_2,V_L_2] :
% 0.94/1.30 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
% 0.94/1.30 => ( V_x_2 != V_y_2
% 0.94/1.30 => ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2))
% 0.94/1.30 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_y_2),V_x_2)),V_L_2)) ) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_Lin__irrefl,axiom,
% 0.94/1.30 ! [V_ba_2,V_aa_2,V_L_2] :
% 0.94/1.30 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_ba_2)),V_L_2))
% 0.94/1.30 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_aa_2)),V_L_2)) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_order__less__irrefl,axiom,
% 0.94/1.30 ! [V_x,T_a] :
% 0.94/1.30 ( class_Orderings_Opreorder(T_a)
% 0.94/1.30 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_linorder__neq__iff,axiom,
% 0.94/1.30 ! [V_y_2,V_x_2,T_a] :
% 0.94/1.30 ( class_Orderings_Olinorder(T_a)
% 0.94/1.30 => ( V_x_2 != V_y_2
% 0.94/1.30 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 0.94/1.30 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_not__less__iff__gr__or__eq,axiom,
% 0.94/1.30 ! [V_y_2,V_x_2,T_a] :
% 0.94/1.30 ( class_Orderings_Olinorder(T_a)
% 0.94/1.30 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 0.94/1.30 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))
% 0.94/1.30 | V_x_2 = V_y_2 ) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_linorder__less__linear,axiom,
% 0.94/1.30 ! [V_y,V_x,T_a] :
% 0.94/1.30 ( class_Orderings_Olinorder(T_a)
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 0.94/1.30 | V_x = V_y
% 0.94/1.30 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_linorder__antisym__conv3,axiom,
% 0.94/1.30 ! [V_x_2,V_y_2,T_a] :
% 0.94/1.30 ( class_Orderings_Olinorder(T_a)
% 0.94/1.30 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2))
% 0.94/1.30 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 0.94/1.30 <=> V_x_2 = V_y_2 ) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_linorder__neqE,axiom,
% 0.94/1.30 ! [V_y,V_x,T_a] :
% 0.94/1.30 ( class_Orderings_Olinorder(T_a)
% 0.94/1.30 => ( V_x != V_y
% 0.94/1.30 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 0.94/1.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_less__imp__neq,axiom,
% 0.94/1.30 ! [V_y,V_x,T_a] :
% 0.94/1.30 ( class_Orderings_Oorder(T_a)
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 0.94/1.30 => V_x != V_y ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_order__less__not__sym,axiom,
% 0.94/1.30 ! [V_y,V_x,T_a] :
% 0.94/1.30 ( class_Orderings_Opreorder(T_a)
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 0.94/1.30 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_order__less__imp__not__less,axiom,
% 0.94/1.30 ! [V_y,V_x,T_a] :
% 0.94/1.30 ( class_Orderings_Opreorder(T_a)
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 0.94/1.30 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_order__less__imp__not__eq,axiom,
% 0.94/1.30 ! [V_y,V_x,T_a] :
% 0.94/1.30 ( class_Orderings_Oorder(T_a)
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 0.94/1.30 => V_x != V_y ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_order__less__imp__not__eq2,axiom,
% 0.94/1.30 ! [V_y,V_x,T_a] :
% 0.94/1.30 ( class_Orderings_Oorder(T_a)
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 0.94/1.30 => V_y != V_x ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_order__less__asym_H,axiom,
% 0.94/1.30 ! [V_b,V_a,T_a] :
% 0.94/1.30 ( class_Orderings_Opreorder(T_a)
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 0.94/1.30 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_xt1_I9_J,axiom,
% 0.94/1.30 ! [V_a,V_b,T_a] :
% 0.94/1.30 ( class_Orderings_Oorder(T_a)
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 0.94/1.30 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_ord__eq__less__trans,axiom,
% 0.94/1.30 ! [V_c,V_b,V_a,T_a] :
% 0.94/1.30 ( class_Orderings_Oord(T_a)
% 0.94/1.30 => ( V_a = V_b
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 0.94/1.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_xt1_I1_J,axiom,
% 0.94/1.30 ! [V_c,V_b,V_a,T_a] :
% 0.94/1.30 ( class_Orderings_Oorder(T_a)
% 0.94/1.30 => ( V_a = V_b
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 0.94/1.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_ord__less__eq__trans,axiom,
% 0.94/1.30 ! [V_c,V_b,V_a,T_a] :
% 0.94/1.30 ( class_Orderings_Oord(T_a)
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 0.94/1.30 => ( V_b = V_c
% 0.94/1.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_xt1_I2_J,axiom,
% 0.94/1.30 ! [V_c,V_a,V_b,T_a] :
% 0.94/1.30 ( class_Orderings_Oorder(T_a)
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 0.94/1.30 => ( V_b = V_c
% 0.94/1.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_order__less__trans,axiom,
% 0.94/1.30 ! [V_z,V_y,V_x,T_a] :
% 0.94/1.30 ( class_Orderings_Opreorder(T_a)
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 0.94/1.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_xt1_I10_J,axiom,
% 0.94/1.30 ! [V_z,V_x,V_y,T_a] :
% 0.94/1.30 ( class_Orderings_Oorder(T_a)
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 0.94/1.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_order__less__asym,axiom,
% 0.94/1.30 ! [V_y,V_x,T_a] :
% 0.94/1.30 ( class_Orderings_Opreorder(T_a)
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 0.94/1.30 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_linorder__cases,axiom,
% 0.94/1.30 ! [V_y,V_x,T_a] :
% 0.94/1.30 ( class_Orderings_Olinorder(T_a)
% 0.94/1.30 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 0.94/1.30 => ( V_x != V_y
% 0.94/1.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_const__Lin__Prof,axiom,
% 0.94/1.30 ! [V_L_2] :
% 0.94/1.30 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
% 0.94/1.30 => hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi),V_L_2)),c_Arrow__Order__Mirabelle_OProf)) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_in__above,axiom,
% 0.94/1.30 ! [V_y_2,V_x_2,V_L_2,V_ba_2,V_aa_2] :
% 0.94/1.30 ( V_aa_2 != V_ba_2
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,V_L_2),V_aa_2),V_ba_2)))
% 0.94/1.30 <=> ( V_x_2 != V_y_2
% 0.94/1.30 & ( V_x_2 = V_ba_2
% 0.94/1.30 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_aa_2),V_y_2)),V_L_2)) )
% 0.94/1.30 & ( V_x_2 != V_ba_2
% 0.94/1.30 => ( ( V_y_2 = V_ba_2
% 0.94/1.30 => ( V_x_2 = V_aa_2
% 0.94/1.30 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_aa_2)),V_L_2)) ) )
% 0.94/1.30 & ( V_y_2 != V_ba_2
% 0.94/1.30 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2)) ) ) ) ) ) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_PiE,axiom,
% 0.94/1.30 ! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 0.94/1.30 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2)))
% 0.94/1.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2)))
% 0.94/1.30 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_funcset__mem,axiom,
% 0.94/1.30 ! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 0.94/1.30 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))))
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 0.94/1.30 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),V_B_2)) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_inv__f__eq,axiom,
% 0.94/1.30 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 0.94/1.30 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 0.94/1.30 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 0.94/1.30 => hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),V_y_2) = V_x_2 ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_inv__f__f,axiom,
% 0.94/1.30 ! [V_x_2,V_f_2,T_b,T_a] :
% 0.94/1.30 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 0.94/1.30 => hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_in__below,axiom,
% 0.94/1.30 ! [V_y_2,V_x_2,V_L_2,V_ba_2,V_aa_2] :
% 0.94/1.30 ( V_aa_2 != V_ba_2
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),c_Arrow__Order__Mirabelle_Obelow(V_L_2,V_aa_2,V_ba_2)))
% 0.94/1.30 <=> ( V_x_2 != V_y_2
% 0.94/1.30 & ( V_y_2 = V_aa_2
% 0.94/1.30 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_ba_2)),V_L_2)) )
% 0.94/1.30 & ( V_y_2 != V_aa_2
% 0.94/1.30 => ( ( V_x_2 = V_aa_2
% 0.94/1.30 => ( V_y_2 = V_ba_2
% 0.94/1.30 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_ba_2),V_y_2)),V_L_2)) ) )
% 0.94/1.30 & ( V_x_2 != V_aa_2
% 0.94/1.30 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),V_x_2),V_y_2)),V_L_2)) ) ) ) ) ) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_inv__into__f__eq,axiom,
% 0.94/1.30 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 0.94/1.30 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 0.94/1.30 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 0.94/1.30 => hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_inv__into__f__f,axiom,
% 0.94/1.30 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 0.94/1.30 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 0.94/1.30 => hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_Pi__mem,axiom,
% 0.94/1.30 ! [V_x_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 0.94/1.30 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2)))
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 0.94/1.30 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_B_2,V_x_2))) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_Pi__UNIV,axiom,
% 0.94/1.30 ! [V_A_2,T_b,T_a] : c_FuncSet_OPi(T_a,T_b,V_A_2,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_funcset__id,axiom,
% 0.94/1.30 ! [V_A_2,T_a] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_a)),c_COMBI(T_a)),c_FuncSet_OPi(T_a,T_a,V_A_2,hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_a),V_A_2)))) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_PiProf,axiom,
% 0.94/1.30 ! [V_na_2] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),V_na_2))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf)) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_psubsetD,axiom,
% 0.94/1.30 ! [V_ca_2,V_B_2,V_A_2,T_a] :
% 0.94/1.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 0.94/1.30 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 0.94/1.30
% 0.94/1.30 fof(fact_below__Lin,axiom,
% 0.94/1.30 ! [V_L_2,V_y_2,V_x_2] :
% 0.94/1.30 ( V_x_2 != V_y_2
% 0.94/1.30 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),V_L_2),c_Arrow__Order__Mirabelle_OLin))
% 0.94/1.30 => hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(V_L_2,V_x_2,V_y_2)),c_Arrow__Order__Mirabelle_OLin)) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_Prof__def,axiom,
% 0.94/1.31 c_Arrow__Order__Mirabelle_OProf = c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_OLin)) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_inj__fun,axiom,
% 0.94/1.31 ! [T_c,V_f_2,T_b,T_a] :
% 0.94/1.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 0.94/1.31 => c_Fun_Oinj__on(T_a,tc_fun(T_c,T_b),hAPP(c_COMBB(T_b,tc_fun(T_c,T_b),T_a,c_COMBK(T_b,T_c)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_dictatorI,axiom,
% 0.94/1.31 ! [V_i_2,V_Fa_2] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),V_Fa_2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin))))
% 0.94/1.31 => ( ! [B_x] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf))
% 0.94/1.31 => ! [B_a,B_b] :
% 0.94/1.31 ( B_a != B_b
% 0.94/1.31 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(B_x,V_i_2)))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),B_a),B_b)),hAPP(V_Fa_2,B_x))) ) ) )
% 0.94/1.31 => c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_n_I2_J,axiom,
% 0.94/1.31 ! [B_m] :
% 0.94/1.31 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),v_n____))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),B_m))),v_Lab____)),v_Lba____)))) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_inj__eq,axiom,
% 0.94/1.31 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 0.94/1.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 0.94/1.31 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 0.94/1.31 <=> V_x_2 = V_y_2 ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_injD,axiom,
% 0.94/1.31 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 0.94/1.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 0.94/1.31 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 0.94/1.31 => V_x_2 = V_y_2 ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_inj__onD,axiom,
% 0.94/1.31 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 0.94/1.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 0.94/1.31 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 0.94/1.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 0.94/1.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 0.94/1.31 => V_x_2 = V_y_2 ) ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_inj__on__iff,axiom,
% 0.94/1.31 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 0.94/1.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 0.94/1.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 0.94/1.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 0.94/1.31 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 0.94/1.31 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_inj__on__contraD,axiom,
% 0.94/1.31 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 0.94/1.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 0.94/1.31 => ( V_x_2 != V_y_2
% 0.94/1.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 0.94/1.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2))
% 0.94/1.31 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact__096a_A_126_061_Ab_096,axiom,
% 0.94/1.31 v_a____ != v_b____ ).
% 0.94/1.31
% 0.94/1.31 fof(fact__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
% 0.94/1.31 hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)) ).
% 0.94/1.31
% 0.94/1.31 fof(fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
% 0.94/1.31 hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_order__refl,axiom,
% 0.94/1.31 ! [V_x,T_a] :
% 0.94/1.31 ( class_Orderings_Opreorder(T_a)
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_x)) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
% 0.94/1.31 ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____)) ).
% 0.94/1.31
% 0.94/1.31 fof(fact__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
% 0.94/1.31 ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_psubset__trans,axiom,
% 0.94/1.31 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 0.94/1.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_le__fun__def,axiom,
% 0.94/1.31 ! [V_g_2,V_f_2,T_a,T_b] :
% 0.94/1.31 ( class_Orderings_Oord(T_b)
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2))
% 0.94/1.31 <=> ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_linorder__linear,axiom,
% 0.94/1.31 ! [V_y,V_x,T_a] :
% 0.94/1.31 ( class_Orderings_Olinorder(T_a)
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 0.94/1.31 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_order__eq__iff,axiom,
% 0.94/1.31 ! [V_y_2,V_x_2,T_a] :
% 0.94/1.31 ( class_Orderings_Oorder(T_a)
% 0.94/1.31 => ( V_x_2 = V_y_2
% 0.94/1.31 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 0.94/1.31 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_order__eq__refl,axiom,
% 0.94/1.31 ! [V_y,V_x,T_a] :
% 0.94/1.31 ( class_Orderings_Opreorder(T_a)
% 0.94/1.31 => ( V_x = V_y
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_le__funD,axiom,
% 0.94/1.31 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 0.94/1.31 ( class_Orderings_Oord(T_b)
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2))
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_order__antisym__conv,axiom,
% 0.94/1.31 ! [V_x_2,V_y_2,T_a] :
% 0.94/1.31 ( class_Orderings_Oorder(T_a)
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2))
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 0.94/1.31 <=> V_x_2 = V_y_2 ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_ord__eq__le__trans,axiom,
% 0.94/1.31 ! [V_c,V_b,V_a,T_a] :
% 0.94/1.31 ( class_Orderings_Oord(T_a)
% 0.94/1.31 => ( V_a = V_b
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c))
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)) ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_xt1_I3_J,axiom,
% 0.94/1.31 ! [V_c,V_b,V_a,T_a] :
% 0.94/1.31 ( class_Orderings_Oorder(T_a)
% 0.94/1.31 => ( V_a = V_b
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_b))
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)) ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_ord__le__eq__trans,axiom,
% 0.94/1.31 ! [V_c,V_b,V_a,T_a] :
% 0.94/1.31 ( class_Orderings_Oord(T_a)
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 0.94/1.31 => ( V_b = V_c
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c)) ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_xt1_I4_J,axiom,
% 0.94/1.31 ! [V_c,V_a,V_b,T_a] :
% 0.94/1.31 ( class_Orderings_Oorder(T_a)
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 0.94/1.31 => ( V_b = V_c
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a)) ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_order__antisym,axiom,
% 0.94/1.31 ! [V_y,V_x,T_a] :
% 0.94/1.31 ( class_Orderings_Oorder(T_a)
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 0.94/1.31 => V_x = V_y ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_order__trans,axiom,
% 0.94/1.31 ! [V_z,V_y,V_x,T_a] :
% 0.94/1.31 ( class_Orderings_Opreorder(T_a)
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z))
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_z)) ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_xt1_I5_J,axiom,
% 0.94/1.31 ! [V_x,V_y,T_a] :
% 0.94/1.31 ( class_Orderings_Oorder(T_a)
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 0.94/1.31 => V_x = V_y ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_xt1_I6_J,axiom,
% 0.94/1.31 ! [V_z,V_x,V_y,T_a] :
% 0.94/1.31 ( class_Orderings_Oorder(T_a)
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y))
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x)) ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_le__funE,axiom,
% 0.94/1.31 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 0.94/1.31 ( class_Orderings_Oord(T_b)
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2))
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_linorder__le__cases,axiom,
% 0.94/1.31 ! [V_y,V_x,T_a] :
% 0.94/1.31 ( class_Orderings_Olinorder(T_a)
% 0.94/1.31 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_linorder__not__less,axiom,
% 0.94/1.31 ! [V_y_2,V_x_2,T_a] :
% 0.94/1.31 ( class_Orderings_Olinorder(T_a)
% 0.94/1.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 0.94/1.31 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_linorder__not__le,axiom,
% 0.94/1.31 ! [V_y_2,V_x_2,T_a] :
% 0.94/1.31 ( class_Orderings_Olinorder(T_a)
% 0.94/1.31 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 0.94/1.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_linorder__le__less__linear,axiom,
% 0.94/1.31 ! [V_y,V_x,T_a] :
% 0.94/1.31 ( class_Orderings_Olinorder(T_a)
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 0.94/1.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_order__less__le,axiom,
% 0.94/1.31 ! [V_y_2,V_x_2,T_a] :
% 0.94/1.31 ( class_Orderings_Oorder(T_a)
% 0.94/1.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 0.94/1.31 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 0.94/1.31 & V_x_2 != V_y_2 ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_less__le__not__le,axiom,
% 0.94/1.31 ! [V_y_2,V_x_2,T_a] :
% 0.94/1.31 ( class_Orderings_Opreorder(T_a)
% 0.94/1.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 0.94/1.31 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 0.94/1.31 & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_order__le__less,axiom,
% 0.94/1.31 ! [V_y_2,V_x_2,T_a] :
% 0.94/1.31 ( class_Orderings_Oorder(T_a)
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 0.94/1.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 0.94/1.31 | V_x_2 = V_y_2 ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_leI,axiom,
% 0.94/1.31 ! [V_y,V_x,T_a] :
% 0.94/1.31 ( class_Orderings_Olinorder(T_a)
% 0.94/1.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_not__leE,axiom,
% 0.94/1.31 ! [V_x,V_y,T_a] :
% 0.94/1.31 ( class_Orderings_Olinorder(T_a)
% 0.94/1.31 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_linorder__antisym__conv1,axiom,
% 0.94/1.31 ! [V_y_2,V_x_2,T_a] :
% 0.94/1.31 ( class_Orderings_Olinorder(T_a)
% 0.94/1.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 0.94/1.31 <=> V_x_2 = V_y_2 ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_order__neq__le__trans,axiom,
% 0.94/1.31 ! [V_b,V_a,T_a] :
% 0.94/1.31 ( class_Orderings_Oorder(T_a)
% 0.94/1.31 => ( V_a != V_b
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_xt1_I12_J,axiom,
% 0.94/1.31 ! [V_b,V_a,T_a] :
% 0.94/1.31 ( class_Orderings_Oorder(T_a)
% 0.94/1.31 => ( V_a != V_b
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_leD,axiom,
% 0.94/1.31 ! [V_x,V_y,T_a] :
% 0.94/1.31 ( class_Orderings_Olinorder(T_a)
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 0.94/1.31 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_order__less__imp__le,axiom,
% 0.94/1.31 ! [V_y,V_x,T_a] :
% 0.94/1.31 ( class_Orderings_Opreorder(T_a)
% 0.94/1.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_linorder__antisym__conv2,axiom,
% 0.94/1.31 ! [V_y_2,V_x_2,T_a] :
% 0.94/1.31 ( class_Orderings_Olinorder(T_a)
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
% 0.94/1.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2))
% 0.94/1.31 <=> V_x_2 = V_y_2 ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_order__le__imp__less__or__eq,axiom,
% 0.94/1.31 ! [V_y,V_x,T_a] :
% 0.94/1.31 ( class_Orderings_Oorder(T_a)
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 0.94/1.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 0.94/1.31 | V_x = V_y ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_order__le__neq__trans,axiom,
% 0.94/1.31 ! [V_b,V_a,T_a] :
% 0.94/1.31 ( class_Orderings_Oorder(T_a)
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 0.94/1.31 => ( V_a != V_b
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_xt1_I11_J,axiom,
% 0.94/1.31 ! [V_a,V_b,T_a] :
% 0.94/1.31 ( class_Orderings_Oorder(T_a)
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 0.94/1.31 => ( V_a != V_b
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_order__less__le__trans,axiom,
% 0.94/1.31 ! [V_z,V_y,V_x,T_a] :
% 0.94/1.31 ( class_Orderings_Opreorder(T_a)
% 0.94/1.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_xt1_I7_J,axiom,
% 0.94/1.31 ! [V_z,V_x,V_y,T_a] :
% 0.94/1.31 ( class_Orderings_Oorder(T_a)
% 0.94/1.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_order__le__less__trans,axiom,
% 0.94/1.31 ! [V_z,V_y,V_x,T_a] :
% 0.94/1.31 ( class_Orderings_Opreorder(T_a)
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
% 0.94/1.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_xt1_I8_J,axiom,
% 0.94/1.31 ! [V_z,V_x,V_y,T_a] :
% 0.94/1.31 ( class_Orderings_Oorder(T_a)
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
% 0.94/1.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_top__greatest,axiom,
% 0.94/1.31 ! [V_x,T_a] :
% 0.94/1.31 ( class_Orderings_Otop(T_a)
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_termination__basic__simps_I5_J,axiom,
% 0.94/1.31 ! [V_y,V_x] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y)) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_inj__on__def,axiom,
% 0.94/1.31 ! [V_A_2,V_f_2,T_b,T_a] :
% 0.94/1.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 0.94/1.31 <=> ! [B_x] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 0.94/1.31 => ! [B_xa] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2))
% 0.94/1.31 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 0.94/1.31 => B_x = B_xa ) ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_mlex__leq,axiom,
% 0.94/1.31 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] :
% 0.94/1.31 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 0.94/1.31 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),V_R_2))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2))) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_inj__on__id2,axiom,
% 0.94/1.31 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_dictator__def,axiom,
% 0.94/1.31 ! [V_i_2,V_Fa_2] :
% 0.94/1.31 ( c_Arrow__Order__Mirabelle_Odictator(V_Fa_2,V_i_2)
% 0.94/1.31 <=> ! [B_x] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),B_x),c_Arrow__Order__Mirabelle_OProf))
% 0.94/1.31 => hAPP(V_Fa_2,B_x) = hAPP(B_x,V_i_2) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
% 0.94/1.31 ~ ! [B_Lab] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),B_Lab))
% 0.94/1.31 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B_Lab),c_Arrow__Order__Mirabelle_OLin)) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
% 0.94/1.31 ~ ! [B_Lba] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),B_Lba))
% 0.94/1.31 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),B_Lba),c_Arrow__Order__Mirabelle_OLin)) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_n_I3_J,axiom,
% 0.94/1.31 hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ).
% 0.94/1.31
% 0.94/1.31 fof(fact__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_096,axiom,
% 0.94/1.31 ? [B_n] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
% 0.94/1.31 & ! [B_m] :
% 0.94/1.31 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),B_m))),v_Lab____)),v_Lba____)))) )
% 0.94/1.31 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_less__or__eq__imp__le,axiom,
% 0.94/1.31 ! [V_n,V_m] :
% 0.94/1.31 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 0.94/1.31 | V_m = V_n )
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_le__neq__implies__less,axiom,
% 0.94/1.31 ! [V_n,V_m] :
% 0.94/1.31 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 0.94/1.31 => ( V_m != V_n
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_less__imp__le__nat,axiom,
% 0.94/1.31 ! [V_n,V_m] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_le__eq__less__or__eq,axiom,
% 0.94/1.31 ! [V_na_2,V_m_2] :
% 0.94/1.31 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2))
% 0.94/1.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
% 0.94/1.31 | V_m_2 = V_na_2 ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_subsetD,axiom,
% 0.94/1.31 ! [V_ca_2,V_B_2,V_A_2,T_a] :
% 0.94/1.31 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 0.94/1.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_Pi__anti__mono,axiom,
% 0.94/1.31 ! [V_B_2,T_b,V_A_2,V_A_H_2,T_a] :
% 0.94/1.31 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_H_2),V_A_2))
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2)),c_FuncSet_OPi(T_a,T_b,V_A_H_2,V_B_2))) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_inj__on__add__nat,axiom,
% 0.94/1.31 ! [V_N_2,V_k_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2),V_N_2) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_add__lessD1,axiom,
% 0.94/1.31 ! [V_k,V_j,V_i] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_less__add__eq__less,axiom,
% 0.94/1.31 ! [V_n,V_m,V_l,V_k] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 0.94/1.31 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_add__less__mono,axiom,
% 0.94/1.31 ! [V_l,V_k,V_j,V_i] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 0.94/1.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_add__less__mono1,axiom,
% 0.94/1.31 ! [V_k,V_j,V_i] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_trans__less__add2,axiom,
% 0.94/1.31 ! [V_m,V_j,V_i] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_trans__less__add1,axiom,
% 0.94/1.31 ! [V_m,V_j,V_i] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_nat__add__left__cancel__less,axiom,
% 0.94/1.31 ! [V_na_2,V_m_2,V_k_2] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_na_2)))
% 0.94/1.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_not__add__less2,axiom,
% 0.94/1.31 ! [V_i,V_j] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i)) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_not__add__less1,axiom,
% 0.94/1.31 ! [V_j,V_i] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i)) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_add__leE,axiom,
% 0.94/1.31 ! [V_n,V_k,V_m] :
% 0.94/1.31 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
% 0.94/1.31 => ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 0.94/1.31 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_add__leD1,axiom,
% 0.94/1.31 ! [V_n,V_k,V_m] :
% 0.94/1.31 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_add__leD2,axiom,
% 0.94/1.31 ! [V_n,V_k,V_m] :
% 0.94/1.31 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_add__le__mono,axiom,
% 0.94/1.31 ! [V_l,V_k,V_j,V_i] :
% 0.94/1.31 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l))
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_add__le__mono1,axiom,
% 0.94/1.31 ! [V_k,V_j,V_i] :
% 0.94/1.31 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_trans__le__add2,axiom,
% 0.94/1.31 ! [V_m,V_j,V_i] :
% 0.94/1.31 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_trans__le__add1,axiom,
% 0.94/1.31 ! [V_m,V_j,V_i] :
% 0.94/1.31 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_nat__add__left__cancel__le,axiom,
% 0.94/1.31 ! [V_na_2,V_m_2,V_k_2] :
% 0.94/1.31 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_na_2)))
% 0.94/1.31 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_le__iff__add,axiom,
% 0.94/1.31 ! [V_na_2,V_m_2] :
% 0.94/1.31 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2))
% 0.94/1.31 <=> ? [B_k] : V_na_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_le__add1,axiom,
% 0.94/1.31 ! [V_m,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_le__add2,axiom,
% 0.94/1.31 ! [V_m,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_nat__add__commute,axiom,
% 0.94/1.31 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_nat__add__left__commute,axiom,
% 0.94/1.31 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z)) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_nat__add__assoc,axiom,
% 0.94/1.31 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_nat__add__left__cancel,axiom,
% 0.94/1.31 ! [V_na_2,V_m_2,V_k_2] :
% 0.94/1.31 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_na_2)
% 0.94/1.31 <=> V_m_2 = V_na_2 ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_nat__add__right__cancel,axiom,
% 0.94/1.31 ! [V_na_2,V_k_2,V_m_2] :
% 0.94/1.31 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_na_2),V_k_2)
% 0.94/1.31 <=> V_m_2 = V_na_2 ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_pred__subset__eq2,axiom,
% 0.94/1.31 ! [V_S_2,V_R_2,T_b,T_a] :
% 0.94/1.31 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a,c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a,c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b,c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a,c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a,c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b,c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_S_2)))
% 0.94/1.31 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_R_2),V_S_2)) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_set__mp,axiom,
% 0.94/1.31 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 0.94/1.31 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 0.94/1.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_set__rev__mp,axiom,
% 0.94/1.31 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_in__mono,axiom,
% 0.94/1.31 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 0.94/1.31 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 0.94/1.31 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_termination__basic__simps_I2_J,axiom,
% 0.94/1.31 ! [V_y,V_z,V_x] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_termination__basic__simps_I1_J,axiom,
% 0.94/1.31 ! [V_z,V_y,V_x] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_termination__basic__simps_I4_J,axiom,
% 0.94/1.31 ! [V_y,V_z,V_x] :
% 0.94/1.31 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_z))
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_termination__basic__simps_I3_J,axiom,
% 0.94/1.31 ! [V_z,V_y,V_x] :
% 0.94/1.31 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y))
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_subset__UNIV,axiom,
% 0.94/1.31 ! [V_A_2,T_a] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_subset__inj__on,axiom,
% 0.94/1.31 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
% 0.94/1.31 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 0.94/1.31 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_less__fun__def,axiom,
% 0.94/1.31 ! [V_g_2,V_f_2,T_a,T_b] :
% 0.94/1.31 ( class_Orderings_Oord(T_b)
% 0.94/1.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2))
% 0.94/1.31 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2),V_g_2))
% 0.94/1.31 & ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2),V_f_2)) ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_psubset__eq,axiom,
% 0.94/1.31 ! [V_B_2,V_A_2,T_a] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 0.94/1.31 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 0.94/1.31 & V_A_2 != V_B_2 ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_subset__iff__psubset__eq,axiom,
% 0.94/1.31 ! [V_B_2,V_A_2,T_a] :
% 0.94/1.31 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 0.94/1.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 0.94/1.31 | V_A_2 = V_B_2 ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_psubset__imp__subset,axiom,
% 0.94/1.31 ! [V_B_2,V_A_2,T_a] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 0.94/1.31 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_psubset__subset__trans,axiom,
% 0.94/1.31 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 0.94/1.31 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_subset__psubset__trans,axiom,
% 0.94/1.31 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 0.94/1.31 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 0.94/1.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_pred__subset__eq,axiom,
% 0.94/1.31 ! [V_S_2,V_R_2,T_a] :
% 0.94/1.31 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_R_2)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2)))
% 0.94/1.31 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_R_2),V_S_2)) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_nat__less__cases,axiom,
% 0.94/1.31 ! [V_Pa_2,V_na_2,V_m_2] :
% 0.94/1.31 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
% 0.94/1.31 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) )
% 0.94/1.31 => ( ( V_m_2 = V_na_2
% 0.94/1.31 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) )
% 0.94/1.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2))
% 0.94/1.31 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) )
% 0.94/1.31 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) ) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_less__not__refl3,axiom,
% 0.94/1.31 ! [V_t,V_s] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 0.94/1.31 => V_s != V_t ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_less__not__refl2,axiom,
% 0.94/1.31 ! [V_m,V_n] :
% 0.94/1.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 0.94/1.31 => V_m != V_n ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_less__irrefl__nat,axiom,
% 0.94/1.31 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_linorder__neqE__nat,axiom,
% 0.94/1.31 ! [V_y,V_x] :
% 0.94/1.31 ( V_x != V_y
% 0.94/1.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 0.94/1.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 0.94/1.31
% 0.94/1.31 fof(fact_nat__neq__iff,axiom,
% 0.94/1.31 ! [V_na_2,V_m_2] :
% 0.94/1.32 ( V_m_2 != V_na_2
% 0.94/1.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
% 0.94/1.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_less__not__refl,axiom,
% 0.94/1.32 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_le__refl,axiom,
% 0.94/1.32 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_n)) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_nat__le__linear,axiom,
% 0.94/1.32 ! [V_n,V_m] :
% 0.94/1.32 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 0.94/1.32 | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_eq__imp__le,axiom,
% 0.94/1.32 ! [V_n,V_m] :
% 0.94/1.32 ( V_m = V_n
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_le__trans,axiom,
% 0.94/1.32 ! [V_k,V_j,V_i] :
% 0.94/1.32 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j),V_k))
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_k)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_le__antisym,axiom,
% 0.94/1.32 ! [V_n,V_m] :
% 0.94/1.32 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
% 0.94/1.32 => V_m = V_n ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_nat__less__le,axiom,
% 0.94/1.32 ! [V_na_2,V_m_2] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
% 0.94/1.32 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2))
% 0.94/1.32 & V_m_2 != V_na_2 ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_059_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
% 0.94/1.32 ~ ! [B_n] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
% 0.94/1.32 => ( ! [B_m] :
% 0.94/1.32 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),B_m))),v_Lab____)),v_Lba____)))) )
% 0.94/1.32 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_less__add__one,axiom,
% 0.94/1.32 ! [V_a,T_a] :
% 0.94/1.32 ( class_Rings_Olinordered__semidom(T_a)
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__le__less__mono,axiom,
% 0.94/1.32 ! [V_d,V_c,V_b,V_a,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__less__le__mono,axiom,
% 0.94/1.32 ! [V_d,V_c,V_b,V_a,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__less__imp__less__left,axiom,
% 0.94/1.32 ! [V_b,V_a,V_c,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__less__imp__less__right,axiom,
% 0.94/1.32 ! [V_b,V_c,V_a,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_equalityI,axiom,
% 0.94/1.32 ! [V_B_2,V_A_2,T_a] :
% 0.94/1.32 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2))
% 0.94/1.32 => V_A_2 = V_B_2 ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_subset__refl,axiom,
% 0.94/1.32 ! [V_A_2,T_a] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_A_2)) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_set__eq__subset,axiom,
% 0.94/1.32 ! [T_a,V_B_2,V_A_2] :
% 0.94/1.32 ( V_A_2 = V_B_2
% 0.94/1.32 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 0.94/1.32 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_rev__predicate1D,axiom,
% 0.94/1.32 ! [V_Q_2,T_a,V_x_2,V_Pa_2] :
% 0.94/1.32 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_Pa_2),V_Q_2))
% 0.94/1.32 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_equalityD1,axiom,
% 0.94/1.32 ! [T_a,V_B_2,V_A_2] :
% 0.94/1.32 ( V_A_2 = V_B_2
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_equalityD2,axiom,
% 0.94/1.32 ! [T_a,V_B_2,V_A_2] :
% 0.94/1.32 ( V_A_2 = V_B_2
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_predicate1D,axiom,
% 0.94/1.32 ! [V_x_2,V_Q_2,V_Pa_2,T_a] :
% 0.94/1.32 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_Pa_2),V_Q_2))
% 0.94/1.32 => ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 0.94/1.32 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_subset__trans,axiom,
% 0.94/1.32 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 0.94/1.32 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2))
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_predicate2D,axiom,
% 0.94/1.32 ! [V_y_2,V_x_2,V_Q_2,V_Pa_2,T_b,T_a] :
% 0.94/1.32 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Q_2))
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 0.94/1.32 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_equalityE,axiom,
% 0.94/1.32 ! [T_a,V_B_2,V_A_2] :
% 0.94/1.32 ( V_A_2 = V_B_2
% 0.94/1.32 => ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 0.94/1.32 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),V_A_2)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_rev__predicate2D,axiom,
% 0.94/1.32 ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_Pa_2] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Q_2))
% 0.94/1.32 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_linorder__neqE__linordered__idom,axiom,
% 0.94/1.32 ! [V_y,V_x,T_a] :
% 0.94/1.32 ( class_Rings_Olinordered__idom(T_a)
% 0.94/1.32 => ( V_x != V_y
% 0.94/1.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__right__imp__eq,axiom,
% 0.94/1.32 ! [V_c,V_a,V_b,T_a] :
% 0.94/1.32 ( class_Groups_Ocancel__semigroup__add(T_a)
% 0.94/1.32 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)
% 0.94/1.32 => V_b = V_c ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__imp__eq,axiom,
% 0.94/1.32 ! [V_c,V_b,V_a,T_a] :
% 0.94/1.32 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 0.94/1.32 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
% 0.94/1.32 => V_b = V_c ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__left__imp__eq,axiom,
% 0.94/1.32 ! [V_c,V_b,V_a,T_a] :
% 0.94/1.32 ( class_Groups_Ocancel__semigroup__add(T_a)
% 0.94/1.32 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
% 0.94/1.32 => V_b = V_c ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__right__cancel,axiom,
% 0.94/1.32 ! [V_ca_2,V_aa_2,V_ba_2,T_a] :
% 0.94/1.32 ( class_Groups_Ocancel__semigroup__add(T_a)
% 0.94/1.32 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_aa_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_aa_2)
% 0.94/1.32 <=> V_ba_2 = V_ca_2 ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__left__cancel,axiom,
% 0.94/1.32 ! [V_ca_2,V_ba_2,V_aa_2,T_a] :
% 0.94/1.32 ( class_Groups_Ocancel__semigroup__add(T_a)
% 0.94/1.32 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_ba_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_ca_2)
% 0.94/1.32 <=> V_ba_2 = V_ca_2 ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.94/1.32 ! [V_c,V_b,V_a,T_a] :
% 0.94/1.32 ( class_Groups_Oab__semigroup__add(T_a)
% 0.94/1.32 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_one__reorient,axiom,
% 0.94/1.32 ! [V_x_2,T_a] :
% 0.94/1.32 ( class_Groups_Oone(T_a)
% 0.94/1.32 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
% 0.94/1.32 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__le__cancel__right,axiom,
% 0.94/1.32 ! [V_ba_2,V_ca_2,V_aa_2,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_ca_2)))
% 0.94/1.32 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2),V_ba_2)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__le__cancel__left,axiom,
% 0.94/1.32 ! [V_ba_2,V_aa_2,V_ca_2,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_aa_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_ba_2)))
% 0.94/1.32 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2),V_ba_2)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__right__mono,axiom,
% 0.94/1.32 ! [V_c,V_b,V_a,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__left__mono,axiom,
% 0.94/1.32 ! [V_c,V_b,V_a,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__mono,axiom,
% 0.94/1.32 ! [V_d,V_c,V_b,V_a,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__le__imp__le__right,axiom,
% 0.94/1.32 ! [V_b,V_c,V_a,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__le__imp__le__left,axiom,
% 0.94/1.32 ! [V_b,V_a,V_c,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__less__cancel__right,axiom,
% 0.94/1.32 ! [V_ba_2,V_ca_2,V_aa_2,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_ca_2)))
% 0.94/1.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__less__cancel__left,axiom,
% 0.94/1.32 ! [V_ba_2,V_aa_2,V_ca_2,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_aa_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_ba_2)))
% 0.94/1.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__strict__right__mono,axiom,
% 0.94/1.32 ! [V_c,V_b,V_a,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__strict__left__mono,axiom,
% 0.94/1.32 ! [V_c,V_b,V_a,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__strict__mono,axiom,
% 0.94/1.32 ! [V_d,V_c,V_b,V_a,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_card__inj,axiom,
% 0.94/1.32 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))))
% 0.94/1.32 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 0.94/1.32 => ( c_Finite__Set_Ofinite(T_b,V_B_2)
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_b,V_B_2))) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_Pi__mono,axiom,
% 0.94/1.32 ! [V_C_2,V_B_2,T_b,V_A_2,T_a] :
% 0.94/1.32 ( ! [B_x] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),hAPP(V_B_2,B_x)),hAPP(V_C_2,B_x))) )
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2)),c_FuncSet_OPi(T_a,T_b,V_A_2,V_C_2))) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_Pi__I,axiom,
% 0.94/1.32 ! [V_B_2,V_f_2,T_b,V_A_2,T_a] :
% 0.94/1.32 ( ! [B_x] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,B_x)),hAPP(V_B_2,B_x))) )
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,V_B_2))) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_card__bij,axiom,
% 0.94/1.32 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))))
% 0.94/1.32 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,T_a)),V_g_2),c_FuncSet_OPi(T_b,T_a,V_B_2,hAPP(c_COMBK(tc_fun(T_a,tc_HOL_Obool),T_b),V_A_2))))
% 0.94/1.32 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2)
% 0.94/1.32 => ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 0.94/1.32 => ( c_Finite__Set_Ofinite(T_b,V_B_2)
% 0.94/1.32 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Finite__Set_Ocard(T_b,V_B_2) ) ) ) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_finite__indi,axiom,
% 0.94/1.32 c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_card__psubset,axiom,
% 0.94/1.32 ! [V_A_2,V_B_2,T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofinite(T_a,V_B_2)
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_a,V_B_2)))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_psubset__card__mono,axiom,
% 0.94/1.32 ! [V_A_2,V_B_2,T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofinite(T_a,V_B_2)
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_a,V_B_2))) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_card__seteq,axiom,
% 0.94/1.32 ! [V_A_2,V_B_2,T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofinite(T_a,V_B_2)
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_B_2)),c_Finite__Set_Ocard(T_a,V_A_2)))
% 0.94/1.32 => V_A_2 = V_B_2 ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_card__mono,axiom,
% 0.94/1.32 ! [V_A_2,V_B_2,T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofinite(T_a,V_B_2)
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_a,V_B_2))) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_finite__code,axiom,
% 0.94/1.32 ! [V_A_2,T_a] :
% 0.94/1.32 ( class_Finite__Set_Ofinite(T_a)
% 0.94/1.32 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_finite,axiom,
% 0.94/1.32 ! [V_A_2,T_a] :
% 0.94/1.32 ( class_Finite__Set_Ofinite(T_a)
% 0.94/1.32 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_card__UNIV__unit,axiom,
% 0.94/1.32 c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_rev__finite__subset,axiom,
% 0.94/1.32 ! [V_A_2,V_B_2,T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofinite(T_a,V_B_2)
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 0.94/1.32 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_finite__subset,axiom,
% 0.94/1.32 ! [V_B_2,V_A_2,T_a] :
% 0.94/1.32 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 0.94/1.32 => ( c_Finite__Set_Ofinite(T_a,V_B_2)
% 0.94/1.32 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_finite__option__UNIV,axiom,
% 0.94/1.32 ! [T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofinite(tc_Option_Ooption(T_a),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool)))
% 0.94/1.32 <=> c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_finite__Plus__UNIV__iff,axiom,
% 0.94/1.32 ! [T_b,T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)))
% 0.94/1.32 <=> ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 0.94/1.32 & c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_finite__Prod__UNIV,axiom,
% 0.94/1.32 ! [T_b,T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 0.94/1.32 => ( c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 0.94/1.32 => c_Finite__Set_Ofinite(tc_prod(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_finite__UNIV,axiom,
% 0.94/1.32 ! [T_a] :
% 0.94/1.32 ( class_Finite__Set_Ofinite(T_a)
% 0.94/1.32 => c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 0.94/1.32 ! [V_A_2,T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 0.94/1.32 => ( c_Finite__Set_Ocard(T_a,V_A_2) = c_Finite__Set_Ocard(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 0.94/1.32 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_finite__fun__UNIVD2,axiom,
% 0.94/1.32 ! [T_b,T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofinite(tc_fun(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)))
% 0.94/1.32 => c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_in__finite__psubset,axiom,
% 0.94/1.32 ! [V_B_2,V_A_2,T_a] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_a)))
% 0.94/1.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 0.94/1.32 & c_Finite__Set_Ofinite(T_a,V_B_2) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_card__Plus,axiom,
% 0.94/1.32 ! [V_B_2,T_b,V_A_2,T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 0.94/1.32 => ( c_Finite__Set_Ofinite(T_b,V_B_2)
% 0.94/1.32 => c_Finite__Set_Ocard(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_b,V_B_2)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_card_Oinsert,axiom,
% 0.94/1.32 ! [V_x_2,V_A_2,T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 0.94/1.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 0.94/1.32 => c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(T_a,V_A_2)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 0.94/1.32 ! [V_B_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 0.94/1.32 => ( c_Finite__Set_Ofinite(T_b,V_A_2)
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2))
% 0.94/1.32 => hAPP(hAPP(V_f_2,hAPP(V_Fa_2,V_B_2)),hAPP(V_Fa_2,V_A_2)) = hAPP(V_Fa_2,V_A_2) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_insertE,axiom,
% 0.94/1.32 ! [V_A_2,V_ba_2,V_aa_2,T_a] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_A_2)))
% 0.94/1.32 => ( V_aa_2 != V_ba_2
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_insertCI,axiom,
% 0.94/1.32 ! [V_ba_2,V_B_2,V_aa_2,T_a] :
% 0.94/1.32 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_B_2))
% 0.94/1.32 => V_aa_2 = V_ba_2 )
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_B_2))) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_finite_OinsertI,axiom,
% 0.94/1.32 ! [V_aa_2,V_A_2,T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 0.94/1.32 => c_Finite__Set_Ofinite(T_a,c_Set_Oinsert(T_a,V_aa_2,V_A_2)) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_finite__insert,axiom,
% 0.94/1.32 ! [V_A_2,V_aa_2,T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofinite(T_a,c_Set_Oinsert(T_a,V_aa_2,V_A_2))
% 0.94/1.32 <=> c_Finite__Set_Ofinite(T_a,V_A_2) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 0.94/1.32 ! [V_x_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 0.94/1.32 => ( c_Finite__Set_Ofinite(T_b,V_A_2)
% 0.94/1.32 => hAPP(V_Fa_2,c_Set_Oinsert(T_b,V_x_2,V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_Fa_2,V_A_2)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 0.94/1.32 ! [V_x_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 0.94/1.32 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_subset__insertI,axiom,
% 0.94/1.32 ! [V_aa_2,V_B_2,T_a] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),c_Set_Oinsert(T_a,V_aa_2,V_B_2))) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_subset__insertI2,axiom,
% 0.94/1.32 ! [V_ba_2,V_B_2,V_A_2,T_a] :
% 0.94/1.32 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Set_Oinsert(T_a,V_ba_2,V_B_2))) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_insert__mono,axiom,
% 0.94/1.32 ! [V_aa_2,V_D_2,V_C_2,T_a] :
% 0.94/1.32 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2),V_D_2))
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_aa_2,V_C_2)),c_Set_Oinsert(T_a,V_aa_2,V_D_2))) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_insertI1,axiom,
% 0.94/1.32 ! [V_B_2,V_aa_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_aa_2,V_B_2))) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_insert__iff,axiom,
% 0.94/1.32 ! [V_A_2,V_ba_2,V_aa_2,T_a] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_A_2)))
% 0.94/1.32 <=> ( V_aa_2 = V_ba_2
% 0.94/1.32 | hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_insert__ident,axiom,
% 0.94/1.32 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 0.94/1.32 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 0.94/1.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 0.94/1.32 => ( c_Set_Oinsert(T_a,V_x_2,V_A_2) = c_Set_Oinsert(T_a,V_x_2,V_B_2)
% 0.94/1.32 <=> V_A_2 = V_B_2 ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_insertI2,axiom,
% 0.94/1.32 ! [V_ba_2,V_B_2,V_aa_2,T_a] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_B_2))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Set_Oinsert(T_a,V_ba_2,V_B_2))) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_insert__absorb,axiom,
% 0.94/1.32 ! [V_A_2,V_aa_2,T_a] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2))
% 0.94/1.32 => c_Set_Oinsert(T_a,V_aa_2,V_A_2) = V_A_2 ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_insert__code,axiom,
% 0.94/1.32 ! [V_x_2,V_A_2,V_y_2,T_a] :
% 0.94/1.32 ( hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_x_2))
% 0.94/1.32 <=> ( V_y_2 = V_x_2
% 0.94/1.32 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_insert__commute,axiom,
% 0.94/1.32 ! [V_A_2,V_y_2,V_x_2,T_a] : c_Set_Oinsert(T_a,V_x_2,c_Set_Oinsert(T_a,V_y_2,V_A_2)) = c_Set_Oinsert(T_a,V_y_2,c_Set_Oinsert(T_a,V_x_2,V_A_2)) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_insert__absorb2,axiom,
% 0.94/1.32 ! [V_A_2,V_x_2,T_a] : c_Set_Oinsert(T_a,V_x_2,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = c_Set_Oinsert(T_a,V_x_2,V_A_2) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_finite__PlusD_I2_J,axiom,
% 0.94/1.32 ! [V_B_2,V_A_2,T_b,T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))
% 0.94/1.32 => c_Finite__Set_Ofinite(T_b,V_B_2) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_finite__PlusD_I1_J,axiom,
% 0.94/1.32 ! [V_B_2,V_A_2,T_b,T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))
% 0.94/1.32 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_finite__Plus,axiom,
% 0.94/1.32 ! [V_B_2,T_b,V_A_2,T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 0.94/1.32 => ( c_Finite__Set_Ofinite(T_b,V_B_2)
% 0.94/1.32 => c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_finite__Plus__iff,axiom,
% 0.94/1.32 ! [V_B_2,V_A_2,T_b,T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))
% 0.94/1.32 <=> ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 0.94/1.32 & c_Finite__Set_Ofinite(T_b,V_B_2) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_subset__insert,axiom,
% 0.94/1.32 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 0.94/1.32 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Set_Oinsert(T_a,V_x_2,V_B_2)))
% 0.94/1.32 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_insert__subset,axiom,
% 0.94/1.32 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 0.94/1.32 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_x_2,V_A_2)),V_B_2))
% 0.94/1.32 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2))
% 0.94/1.32 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_card__insert__le,axiom,
% 0.94/1.32 ! [V_x_2,V_A_2,T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2)))) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 0.94/1.32 ! [V_x_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 0.94/1.32 => ( c_Finite__Set_Ofinite(T_b,V_A_2)
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 0.94/1.32 => hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_Fa_2,V_A_2)) = hAPP(V_Fa_2,V_A_2) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_UNIV__Plus__UNIV,axiom,
% 0.94/1.32 ! [T_b,T_a] : c_Sum__Type_OPlus(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_card__Plus__conv__if,axiom,
% 0.94/1.32 ! [V_B_2,T_b,V_A_2,T_a] :
% 0.94/1.32 ( ( ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 0.94/1.32 & c_Finite__Set_Ofinite(T_b,V_B_2) )
% 0.94/1.32 => c_Finite__Set_Ocard(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_b,V_B_2)) )
% 0.94/1.32 & ( ~ ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 0.94/1.32 & c_Finite__Set_Ofinite(T_b,V_B_2) )
% 0.94/1.32 => c_Finite__Set_Ocard(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_folding__image__simple_Oinsert,axiom,
% 0.94/1.32 ! [V_x_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 0.94/1.32 => ( c_Finite__Set_Ofinite(T_b,V_A_2)
% 0.94/1.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 0.94/1.32 => hAPP(V_Fa_2,c_Set_Oinsert(T_b,V_x_2,V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_Fa_2,V_A_2)) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_max__extp__max__ext__eq,axiom,
% 0.94/1.32 ! [V_xa_2,V_x_2,V_R_2,T_a] :
% 0.94/1.32 ( c_Wellfounded_Omax__extp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_a,c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(T_a,tc_prod(T_a,T_a)),tc_fun(T_a,tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool)),T_a,c_COMBB(tc_prod(T_a,T_a),tc_fun(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_HOL_Obool),T_a,c_member(tc_prod(T_a,T_a)))),c_Product__Type_OPair(T_a,T_a)))),V_R_2),V_x_2,V_xa_2)
% 0.94/1.32 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_less__zeroE,axiom,
% 0.94/1.32 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_le0,axiom,
% 0.94/1.32 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_le__0__eq,axiom,
% 0.94/1.32 ! [V_na_2] :
% 0.94/1.32 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_na_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 0.94/1.32 <=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 0.94/1.32 ! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_plus__nat_Oadd__0,axiom,
% 0.94/1.32 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 0.94/1.32
% 0.94/1.32 fof(fact_Nat_Oadd__0__right,axiom,
% 0.94/1.32 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__is__0,axiom,
% 0.94/1.32 ! [V_na_2,V_m_2] :
% 0.94/1.32 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 0.94/1.32 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 0.94/1.32 & V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__eq__self__zero,axiom,
% 0.94/1.32 ! [V_n,V_m] :
% 0.94/1.32 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 0.94/1.32 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_gr0I,axiom,
% 0.94/1.32 ! [V_n] :
% 0.94/1.32 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_gr__implies__not0,axiom,
% 0.94/1.32 ! [V_n,V_m] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 0.94/1.32 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_less__nat__zero__code,axiom,
% 0.94/1.32 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_neq0__conv,axiom,
% 0.94/1.32 ! [V_na_2] :
% 0.94/1.32 ( V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 0.94/1.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_not__less0,axiom,
% 0.94/1.32 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_zero__reorient,axiom,
% 0.94/1.32 ! [V_x_2,T_a] :
% 0.94/1.32 ( class_Groups_Ozero(T_a)
% 0.94/1.32 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
% 0.94/1.32 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add_Ocomm__neutral,axiom,
% 0.94/1.32 ! [V_a,T_a] :
% 0.94/1.32 ( class_Groups_Ocomm__monoid__add(T_a)
% 0.94/1.32 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__0__right,axiom,
% 0.94/1.32 ! [V_a,T_a] :
% 0.94/1.32 ( class_Groups_Omonoid__add(T_a)
% 0.94/1.32 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_double__zero__sym,axiom,
% 0.94/1.32 ! [V_aa_2,T_a] :
% 0.94/1.32 ( class_Groups_Olinordered__ab__group__add(T_a)
% 0.94/1.32 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)
% 0.94/1.32 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__0,axiom,
% 0.94/1.32 ! [V_a,T_a] :
% 0.94/1.32 ( class_Groups_Ocomm__monoid__add(T_a)
% 0.94/1.32 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__0__left,axiom,
% 0.94/1.32 ! [V_a,T_a] :
% 0.94/1.32 ( class_Groups_Omonoid__add(T_a)
% 0.94/1.32 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_zero__neq__one,axiom,
% 0.94/1.32 ! [T_a] :
% 0.94/1.32 ( class_Rings_Ozero__neq__one(T_a)
% 0.94/1.32 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_one__neq__zero,axiom,
% 0.94/1.32 ! [T_a] :
% 0.94/1.32 ( class_Rings_Ozero__neq__one(T_a)
% 0.94/1.32 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.94/1.32 ! [V_aa_2,T_a] :
% 0.94/1.32 ( class_Groups_Olinordered__ab__group__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)))
% 0.94/1.32 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_aa_2)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.94/1.32 ! [V_aa_2,T_a] :
% 0.94/1.32 ( class_Groups_Olinordered__ab__group__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 0.94/1.32 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__nonneg__nonneg,axiom,
% 0.94/1.32 ! [V_b,V_a,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__nonneg__eq__0__iff,axiom,
% 0.94/1.32 ! [V_y_2,V_x_2,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x_2))
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y_2))
% 0.94/1.32 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 0.94/1.32 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 0.94/1.32 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__increasing,axiom,
% 0.94/1.32 ! [V_c,V_b,V_a,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c))
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__increasing2,axiom,
% 0.94/1.32 ! [V_a,V_b,V_c,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__nonpos__nonpos,axiom,
% 0.94/1.32 ! [V_b,V_a,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__neg__neg,axiom,
% 0.94/1.32 ! [V_b,V_a,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_pos__add__strict,axiom,
% 0.94/1.32 ! [V_c,V_b,V_a,T_a] :
% 0.94/1.32 ( class_Rings_Olinordered__semidom(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__pos__pos,axiom,
% 0.94/1.32 ! [V_b,V_a,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.94/1.32 ! [V_aa_2,T_a] :
% 0.94/1.32 ( class_Groups_Olinordered__ab__group__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 0.94/1.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.94/1.32 ! [V_aa_2,T_a] :
% 0.94/1.32 ( class_Groups_Olinordered__ab__group__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)))
% 0.94/1.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_aa_2)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_not__one__le__zero,axiom,
% 0.94/1.32 ! [T_a] :
% 0.94/1.32 ( class_Rings_Olinordered__semidom(T_a)
% 0.94/1.32 => ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_zero__le__one,axiom,
% 0.94/1.32 ! [T_a] :
% 0.94/1.32 ( class_Rings_Olinordered__semidom(T_a)
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_zero__less__one,axiom,
% 0.94/1.32 ! [T_a] :
% 0.94/1.32 ( class_Rings_Olinordered__semidom(T_a)
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_not__one__less__zero,axiom,
% 0.94/1.32 ! [T_a] :
% 0.94/1.32 ( class_Rings_Olinordered__semidom(T_a)
% 0.94/1.32 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__gr__0,axiom,
% 0.94/1.32 ! [V_na_2,V_m_2] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2)))
% 0.94/1.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 0.94/1.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_card__infinite,axiom,
% 0.94/1.32 ! [V_A_2,T_a] :
% 0.94/1.32 ( ~ c_Finite__Set_Ofinite(T_a,V_A_2)
% 0.94/1.32 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__nonpos__neg,axiom,
% 0.94/1.32 ! [V_b,V_a,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__neg__nonpos,axiom,
% 0.94/1.32 ! [V_b,V_a,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__strict__increasing2,axiom,
% 0.94/1.32 ! [V_c,V_b,V_a,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__strict__increasing,axiom,
% 0.94/1.32 ! [V_c,V_b,V_a,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__nonneg__pos,axiom,
% 0.94/1.32 ! [V_b,V_a,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__pos__nonneg,axiom,
% 0.94/1.32 ! [V_b,V_a,T_a] :
% 0.94/1.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 0.94/1.32 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_zero__less__two,axiom,
% 0.94/1.32 ! [T_a] :
% 0.94/1.32 ( class_Rings_Olinordered__semidom(T_a)
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_card__ge__0__finite,axiom,
% 0.94/1.32 ! [V_A_2,T_a] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(T_a,V_A_2)))
% 0.94/1.32 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_finite__UNIV__card__ge__0,axiom,
% 0.94/1.32 ! [T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_even__less__0__iff,axiom,
% 0.94/1.32 ! [V_aa_2,T_a] :
% 0.94/1.32 ( class_Rings_Olinordered__idom(T_a)
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 0.94/1.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_finite__fun__UNIVD1,axiom,
% 0.94/1.32 ! [T_b,T_a] :
% 0.94/1.32 ( c_Finite__Set_Ofinite(tc_fun(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)))
% 0.94/1.32 => ( c_Finite__Set_Ocard(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 0.94/1.32 => c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_double__eq__0__iff,axiom,
% 0.94/1.32 ! [V_aa_2,T_a] :
% 0.94/1.32 ( class_Groups_Olinordered__ab__group__add(T_a)
% 0.94/1.32 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 0.94/1.32 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_Suc__mono,axiom,
% 0.94/1.32 ! [V_n,V_m] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_lessI,axiom,
% 0.94/1.32 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_zero__less__Suc,axiom,
% 0.94/1.32 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_n))) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_Zero__not__Suc,axiom,
% 0.94/1.32 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_nat_Osimps_I2_J,axiom,
% 0.94/1.32 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_Suc__not__Zero,axiom,
% 0.94/1.32 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_nat_Osimps_I3_J,axiom,
% 0.94/1.32 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_Zero__neq__Suc,axiom,
% 0.94/1.32 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_Suc__neq__Zero,axiom,
% 0.94/1.32 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_not__less__eq,axiom,
% 0.94/1.32 ! [V_na_2,V_m_2] :
% 0.94/1.32 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
% 0.94/1.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_less__Suc__eq,axiom,
% 0.94/1.32 ! [V_na_2,V_m_2] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2)))
% 0.94/1.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
% 0.94/1.32 | V_m_2 = V_na_2 ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_Suc__less__eq,axiom,
% 0.94/1.32 ! [V_na_2,V_m_2] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_na_2)))
% 0.94/1.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_not__less__less__Suc__eq,axiom,
% 0.94/1.32 ! [V_m_2,V_na_2] :
% 0.94/1.32 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2))
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2)))
% 0.94/1.32 <=> V_na_2 = V_m_2 ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_less__antisym,axiom,
% 0.94/1.32 ! [V_m,V_n] :
% 0.94/1.32 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 0.94/1.32 => V_m = V_n ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_less__SucI,axiom,
% 0.94/1.32 ! [V_n,V_m] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_Suc__lessI,axiom,
% 0.94/1.32 ! [V_n,V_m] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 0.94/1.32 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_less__trans__Suc,axiom,
% 0.94/1.32 ! [V_k,V_j,V_i] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_less__SucE,axiom,
% 0.94/1.32 ! [V_n,V_m] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 0.94/1.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 0.94/1.32 => V_m = V_n ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_Suc__lessD,axiom,
% 0.94/1.32 ! [V_n,V_m] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_Suc__less__SucD,axiom,
% 0.94/1.32 ! [V_n,V_m] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__Suc__shift,axiom,
% 0.94/1.32 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__Suc,axiom,
% 0.94/1.32 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__Suc__right,axiom,
% 0.94/1.32 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_Suc__n__not__le__n,axiom,
% 0.94/1.32 ! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_not__less__eq__eq,axiom,
% 0.94/1.32 ! [V_na_2,V_m_2] :
% 0.94/1.32 ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2))
% 0.94/1.32 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_2)),V_m_2)) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_le__Suc__eq,axiom,
% 0.94/1.32 ! [V_na_2,V_m_2] :
% 0.94/1.32 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_na_2)))
% 0.94/1.32 <=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2))
% 0.94/1.32 | V_m_2 = hAPP(c_Nat_OSuc,V_na_2) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_Suc__le__mono,axiom,
% 0.94/1.32 ! [V_m_2,V_na_2] :
% 0.94/1.32 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_2)),hAPP(c_Nat_OSuc,V_m_2)))
% 0.94/1.32 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_na_2),V_m_2)) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_le__SucI,axiom,
% 0.94/1.32 ! [V_n,V_m] :
% 0.94/1.32 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_le__SucE,axiom,
% 0.94/1.32 ! [V_n,V_m] :
% 0.94/1.32 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n)))
% 0.94/1.32 => ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 0.94/1.32 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_Suc__leD,axiom,
% 0.94/1.32 ! [V_n,V_m] :
% 0.94/1.32 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n))
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_Suc__inject,axiom,
% 0.94/1.32 ! [V_y,V_x] :
% 0.94/1.32 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 0.94/1.32 => V_x = V_y ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_nat_Oinject,axiom,
% 0.94/1.32 ! [V_nat_H_2,V_nat_2] :
% 0.94/1.32 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 0.94/1.32 <=> V_nat_2 = V_nat_H_2 ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_Suc__n__not__n,axiom,
% 0.94/1.32 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 0.94/1.32
% 0.94/1.32 fof(fact_n__not__Suc__n,axiom,
% 0.94/1.32 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_inj__Suc,axiom,
% 0.94/1.32 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_gr0__conv__Suc,axiom,
% 0.94/1.32 ! [V_na_2] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2))
% 0.94/1.32 <=> ? [B_m] : V_na_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_less__Suc0,axiom,
% 0.94/1.32 ! [V_na_2] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 0.94/1.32 <=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_less__Suc__eq__0__disj,axiom,
% 0.94/1.32 ! [V_na_2,V_m_2] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2)))
% 0.94/1.32 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 0.94/1.32 | ? [B_j] :
% 0.94/1.32 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 0.94/1.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_na_2)) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_one__is__add,axiom,
% 0.94/1.32 ! [V_na_2,V_m_2] :
% 0.94/1.32 ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2)
% 0.94/1.32 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 0.94/1.32 & V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 0.94/1.32 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 0.94/1.32 & V_na_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_add__is__1,axiom,
% 0.94/1.32 ! [V_na_2,V_m_2] :
% 0.94/1.32 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 0.94/1.32 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 0.94/1.32 & V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 0.94/1.32 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 0.94/1.32 & V_na_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_less__add__Suc1,axiom,
% 0.94/1.32 ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_less__add__Suc2,axiom,
% 0.94/1.32 ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_less__iff__Suc__add,axiom,
% 0.94/1.32 ! [V_na_2,V_m_2] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
% 0.94/1.32 <=> ? [B_k] : V_na_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_Suc__le__lessD,axiom,
% 0.94/1.32 ! [V_n,V_m] :
% 0.94/1.32 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_le__less__Suc__eq,axiom,
% 0.94/1.32 ! [V_na_2,V_m_2] :
% 0.94/1.32 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2))
% 0.94/1.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2)))
% 0.94/1.32 <=> V_na_2 = V_m_2 ) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_Suc__leI,axiom,
% 0.94/1.32 ! [V_n,V_m] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 0.94/1.32 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_le__imp__less__Suc,axiom,
% 0.94/1.32 ! [V_n,V_m] :
% 0.94/1.32 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
% 0.94/1.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_Suc__le__eq,axiom,
% 0.94/1.32 ! [V_na_2,V_m_2] :
% 0.94/1.32 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_na_2))
% 0.94/1.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_less__Suc__eq__le,axiom,
% 0.94/1.32 ! [V_na_2,V_m_2] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2)))
% 0.94/1.32 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_less__eq__Suc__le,axiom,
% 0.94/1.32 ! [V_m_2,V_na_2] :
% 0.94/1.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2))
% 0.94/1.32 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_2)),V_m_2)) ) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_One__nat__def,axiom,
% 0.94/1.32 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_less__eq__Suc__le__raw,axiom,
% 0.94/1.32 ! [V_na_2] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_2)) ).
% 0.94/1.32
% 0.94/1.32 fof(fact_card__insert__disjoint,axiom,
% 0.94/1.32 ! [V_x_2,V_A_2,T_a] :
% 0.94/1.33 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 0.94/1.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 0.94/1.33 => c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(T_a,V_A_2)) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_card__insert__if,axiom,
% 0.94/1.33 ! [V_x_2,V_A_2,T_a] :
% 0.94/1.33 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 0.94/1.33 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 0.94/1.33 => c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = c_Finite__Set_Ocard(T_a,V_A_2) )
% 0.94/1.33 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 0.94/1.33 => c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(T_a,V_A_2)) ) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_Suc__eq__plus1,axiom,
% 0.94/1.33 ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_Suc__eq__plus1__left,axiom,
% 0.94/1.33 ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_nat_Osize_I2_J,axiom,
% 0.94/1.33 ! [V_nat] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_nat_Osize_I1_J,axiom,
% 0.94/1.33 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_nat_Osize_I4_J,axiom,
% 0.94/1.33 ! [V_nat] : c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_Ints__odd__less__0,axiom,
% 0.94/1.33 ! [V_aa_2,T_a] :
% 0.94/1.33 ( class_Rings_Olinordered__idom(T_a)
% 0.94/1.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Int_Oring__1__class_OInts(T_a)))
% 0.94/1.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),V_aa_2)),V_aa_2)),c_Groups_Ozero__class_Ozero(T_a)))
% 0.94/1.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_nat__size,axiom,
% 0.94/1.33 ! [V_n] : c_Nat_Osize__class_Osize(tc_Nat_Onat,V_n) = V_n ).
% 0.94/1.33
% 0.94/1.33 fof(fact_Ints__0,axiom,
% 0.94/1.33 ! [T_a] :
% 0.94/1.33 ( class_Rings_Oring__1(T_a)
% 0.94/1.33 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_Ints__add,axiom,
% 0.94/1.33 ! [V_ba_2,V_aa_2,T_a] :
% 0.94/1.33 ( class_Rings_Oring__1(T_a)
% 0.94/1.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Int_Oring__1__class_OInts(T_a)))
% 0.94/1.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Int_Oring__1__class_OInts(T_a)))
% 0.94/1.33 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_ba_2)),c_Int_Oring__1__class_OInts(T_a))) ) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_nat_Osize_I3_J,axiom,
% 0.94/1.33 c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_Ints__1,axiom,
% 0.94/1.33 ! [T_a] :
% 0.94/1.33 ( class_Rings_Oring__1(T_a)
% 0.94/1.33 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_Ints__double__eq__0__iff,axiom,
% 0.94/1.33 ! [V_aa_2,T_a] :
% 0.94/1.33 ( class_Int_Oring__char__0(T_a)
% 0.94/1.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Int_Oring__1__class_OInts(T_a)))
% 0.94/1.33 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
% 0.94/1.33 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_Ints__odd__nonzero,axiom,
% 0.94/1.33 ! [V_aa_2,T_a] :
% 0.94/1.33 ( class_Int_Oring__char__0(T_a)
% 0.94/1.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),c_Int_Oring__1__class_OInts(T_a)))
% 0.94/1.33 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),V_aa_2)),V_aa_2) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 0.94/1.33 ! [V_a,T_a] :
% 0.94/1.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.94/1.33 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 0.94/1.33 ! [V_a,T_a] :
% 0.94/1.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.94/1.33 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 0.94/1.33 ! [V_d,V_c,V_b,V_a,T_a] :
% 0.94/1.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.94/1.33 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 0.94/1.33 ! [V_c,V_b,V_a,T_a] :
% 0.94/1.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.94/1.33 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 0.94/1.33 ! [V_c,V_b,V_a,T_a] :
% 0.94/1.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.94/1.33 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 0.94/1.33 ! [V_d,V_c,V_a,T_a] :
% 0.94/1.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.94/1.33 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 0.94/1.33 ! [V_d,V_c,V_a,T_a] :
% 0.94/1.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.94/1.33 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d)) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 0.94/1.33 ! [V_c,V_a,T_a] :
% 0.94/1.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 0.94/1.33 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_add__0__iff,axiom,
% 0.94/1.33 ! [V_aa_2,V_ba_2,T_a] :
% 0.94/1.33 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 0.94/1.33 => ( V_ba_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_aa_2)
% 0.94/1.33 <=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_ex__least__nat__less,axiom,
% 0.94/1.33 ! [V_na_2,V_Pa_2] :
% 0.94/1.33 ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 0.94/1.33 => ( hBOOL(hAPP(V_Pa_2,V_na_2))
% 0.94/1.33 => ? [B_k] :
% 0.94/1.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_na_2))
% 0.94/1.33 & ! [B_i] :
% 0.94/1.33 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i),B_k))
% 0.94/1.33 => ~ hBOOL(hAPP(V_Pa_2,B_i)) )
% 0.94/1.33 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_card_Oeq__fold__g,axiom,
% 0.94/1.33 ! [V_A_2,T_a] :
% 0.94/1.33 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 0.94/1.33 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Finite__Set_Ofold__image(tc_Nat_Onat,T_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_A_2) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 0.94/1.33 ! [V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 0.94/1.33 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 0.94/1.33 => ( c_Finite__Set_Ofinite(T_b,V_A_2)
% 0.94/1.33 => hAPP(V_Fa_2,V_A_2) = c_Finite__Set_Ofold__image(T_a,T_b,V_f_2,V_g_2,V_z_2,V_A_2) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_card__def,axiom,
% 0.94/1.33 ! [V_A_2,T_a] :
% 0.94/1.33 ( ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 0.94/1.33 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Finite__Set_Ofold__image(tc_Nat_Onat,T_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_A_2) )
% 0.94/1.33 & ( ~ c_Finite__Set_Ofinite(T_a,V_A_2)
% 0.94/1.33 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_surjh,axiom,
% 0.94/1.33 c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 0.94/1.33 ! [V_na_2,V_m_2] :
% 0.94/1.33 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_na_2))
% 0.94/1.33 <=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_na_2)) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_image__eqI,axiom,
% 0.94/1.33 ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_ba_2] :
% 0.94/1.33 ( V_ba_2 = hAPP(V_f_2,V_x_2)
% 0.94/1.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 0.94/1.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_finite__imageI,axiom,
% 0.94/1.33 ! [V_ha_2,T_b,V_Fa_2,T_a] :
% 0.94/1.33 ( c_Finite__Set_Ofinite(T_a,V_Fa_2)
% 0.94/1.33 => c_Finite__Set_Ofinite(T_b,c_Set_Oimage(T_a,T_b,V_ha_2,V_Fa_2)) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_range__ex1__eq,axiom,
% 0.94/1.33 ! [V_ba_2,V_f_2,T_b,T_a] :
% 0.94/1.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 0.94/1.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Set_Oimage(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))))
% 0.94/1.33 <=> ? [B_x] :
% 0.94/1.33 ( V_ba_2 = hAPP(V_f_2,B_x)
% 0.94/1.33 & ! [B_y] :
% 0.94/1.33 ( V_ba_2 = hAPP(V_f_2,B_y)
% 0.94/1.33 => B_y = B_x ) ) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_inj__image__mem__iff,axiom,
% 0.94/1.33 ! [V_A_2,V_aa_2,V_f_2,T_b,T_a] :
% 0.94/1.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 0.94/1.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_aa_2)),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)))
% 0.94/1.33 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_aa_2),V_A_2)) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_endo__inj__surj,axiom,
% 0.94/1.33 ! [V_f_2,V_A_2,T_a] :
% 0.94/1.33 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 0.94/1.33 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_a,T_a,V_f_2,V_A_2)),V_A_2))
% 0.94/1.33 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2)
% 0.94/1.33 => c_Set_Oimage(T_a,T_a,V_f_2,V_A_2) = V_A_2 ) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_finite__surj__inj,axiom,
% 0.94/1.33 ! [V_f_2,V_A_2,T_a] :
% 0.94/1.33 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 0.94/1.33 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Set_Oimage(T_a,T_a,V_f_2,V_A_2)))
% 0.94/1.33 => c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_finite__UNIV__surj__inj,axiom,
% 0.94/1.33 ! [V_f_2,T_a] :
% 0.94/1.33 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 0.94/1.33 => ( c_Set_Oimage(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
% 0.94/1.33 => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_finite__UNIV__inj__surj,axiom,
% 0.94/1.33 ! [V_f_2,T_a] :
% 0.94/1.33 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 0.94/1.33 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 0.94/1.33 => c_Set_Oimage(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_inj__image__subset__iff,axiom,
% 0.94/1.33 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 0.94/1.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 0.94/1.33 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),c_Set_Oimage(T_a,T_b,V_f_2,V_B_2)))
% 0.94/1.33 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_card__image__le,axiom,
% 0.94/1.33 ! [V_f_2,T_b,V_A_2,T_a] :
% 0.94/1.33 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 0.94/1.33 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))),c_Finite__Set_Ocard(T_a,V_A_2))) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_eq__card__imp__inj__on,axiom,
% 0.94/1.33 ! [V_f_2,T_b,V_A_2,T_a] :
% 0.94/1.33 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 0.94/1.33 => ( c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = c_Finite__Set_Ocard(T_a,V_A_2)
% 0.94/1.33 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_inj__on__iff__eq__card,axiom,
% 0.94/1.33 ! [V_f_2,T_b,V_A_2,T_a] :
% 0.94/1.33 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 0.94/1.33 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 0.94/1.33 <=> c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = c_Finite__Set_Ocard(T_a,V_A_2) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_insert__image,axiom,
% 0.94/1.33 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 0.94/1.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 0.94/1.33 => c_Set_Oinsert(T_b,hAPP(V_f_2,V_x_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = c_Set_Oimage(T_a,T_b,V_f_2,V_A_2) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_rangeI,axiom,
% 0.94/1.33 ! [T_b,V_x_2,V_f_2,T_a] : hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_x_2)),c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_range__eqI,axiom,
% 0.94/1.33 ! [T_b,T_a,V_x_2,V_f_2,V_ba_2] :
% 0.94/1.33 ( V_ba_2 = hAPP(V_f_2,V_x_2)
% 0.94/1.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_ba_2),c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_finite__surj,axiom,
% 0.94/1.33 ! [V_f_2,V_B_2,T_b,V_A_2,T_a] :
% 0.94/1.33 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 0.94/1.33 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),V_B_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)))
% 0.94/1.33 => c_Finite__Set_Ofinite(T_b,V_B_2) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_finite__imageD,axiom,
% 0.94/1.33 ! [V_A_2,V_f_2,T_b,T_a] :
% 0.94/1.33 ( c_Finite__Set_Ofinite(T_a,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))
% 0.94/1.33 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2)
% 0.94/1.33 => c_Finite__Set_Ofinite(T_b,V_A_2) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_inj__image__eq__iff,axiom,
% 0.94/1.33 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 0.94/1.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 0.94/1.33 => ( c_Set_Oimage(T_a,T_b,V_f_2,V_A_2) = c_Set_Oimage(T_a,T_b,V_f_2,V_B_2)
% 0.94/1.33 <=> V_A_2 = V_B_2 ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_card__image,axiom,
% 0.94/1.33 ! [V_A_2,V_f_2,T_b,T_a] :
% 0.94/1.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 0.94/1.33 => c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = c_Finite__Set_Ocard(T_a,V_A_2) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_f__inv__into__f,axiom,
% 0.94/1.33 ! [V_A_2,V_f_2,T_b,V_y_2,T_a] :
% 0.94/1.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)))
% 0.94/1.33 => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_a,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_inv__into__into,axiom,
% 0.94/1.33 ! [V_A_2,V_f_2,T_b,V_x_2,T_a] :
% 0.94/1.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)))
% 0.94/1.33 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_a,V_A_2,V_f_2),V_x_2)),V_A_2)) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_inv__into__injective,axiom,
% 0.94/1.33 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_b,T_a] :
% 0.94/1.33 ( hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),V_x_2) = hAPP(c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),V_y_2)
% 0.94/1.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)))
% 0.94/1.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)))
% 0.94/1.33 => V_x_2 = V_y_2 ) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_image__inv__into__cancel,axiom,
% 0.94/1.33 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_a,T_b] :
% 0.94/1.33 ( c_Set_Oimage(T_b,T_a,V_f_2,V_A_2) = V_A_H_2
% 0.94/1.33 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_H_2),V_A_H_2))
% 0.94/1.33 => c_Set_Oimage(T_b,T_a,V_f_2,c_Set_Oimage(T_a,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_a,V_A_2,V_f_2),V_B_H_2)) = V_B_H_2 ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_surj__iff__all,axiom,
% 0.94/1.33 ! [V_f_2,T_a,T_b] :
% 0.94/1.33 ( c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
% 0.94/1.33 <=> ! [B_x] : hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_a,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),B_x)) = B_x ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_surj__f__inv__f,axiom,
% 0.94/1.33 ! [V_y_2,V_f_2,T_a,T_b] :
% 0.94/1.33 ( c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
% 0.94/1.33 => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_a,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2)) = V_y_2 ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_image__surj__f__inv__f,axiom,
% 0.94/1.33 ! [V_A_2,V_f_2,T_a,T_b] :
% 0.94/1.33 ( c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
% 0.94/1.33 => c_Set_Oimage(T_b,T_a,V_f_2,c_Set_Oimage(T_a,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_a,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_A_2)) = V_A_2 ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_inj__on__strict__subset,axiom,
% 0.94/1.33 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
% 0.94/1.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 0.94/1.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))
% 0.94/1.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),c_Set_Oimage(T_a,T_b,V_f_2,V_B_2))) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_image__iff,axiom,
% 0.94/1.33 ! [V_A_2,V_f_2,T_b,V_z_2,T_a] :
% 0.94/1.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)))
% 0.94/1.33 <=> ? [B_x] :
% 0.94/1.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 0.94/1.33 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_imageI,axiom,
% 0.94/1.33 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 0.94/1.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 0.94/1.33 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_rev__image__eqI,axiom,
% 0.94/1.33 ! [T_b,V_f_2,V_ba_2,V_A_2,V_x_2,T_a] :
% 0.94/1.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2))
% 0.94/1.33 => ( V_ba_2 = hAPP(V_f_2,V_x_2)
% 0.94/1.33 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_image__insert,axiom,
% 0.94/1.33 ! [V_B_2,V_aa_2,V_f_2,T_a,T_b] : c_Set_Oimage(T_b,T_a,V_f_2,c_Set_Oinsert(T_b,V_aa_2,V_B_2)) = c_Set_Oinsert(T_a,hAPP(V_f_2,V_aa_2),c_Set_Oimage(T_b,T_a,V_f_2,V_B_2)) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_range__composition,axiom,
% 0.94/1.33 ! [V_g_2,V_f_2,T_c,T_a,T_b] : c_Set_Oimage(T_b,T_a,hAPP(c_COMBB(T_c,T_a,T_b,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Set_Oimage(T_c,T_a,V_f_2,c_Set_Oimage(T_b,T_c,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_image__image,axiom,
% 0.94/1.33 ! [V_A_2,V_g_2,T_c,V_f_2,T_a,T_b] : c_Set_Oimage(T_b,T_a,V_f_2,c_Set_Oimage(T_c,T_b,V_g_2,V_A_2)) = c_Set_Oimage(T_c,T_a,hAPP(c_COMBB(T_b,T_a,T_c,V_f_2),V_g_2),V_A_2) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_image__ident,axiom,
% 0.94/1.33 ! [V_Y_2,T_a] : c_Set_Oimage(T_a,T_a,c_COMBI(T_a),V_Y_2) = V_Y_2 ).
% 0.94/1.33
% 0.94/1.33 fof(fact_image__mono,axiom,
% 0.94/1.33 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] :
% 0.94/1.33 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))
% 0.94/1.33 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),c_Set_Oimage(T_a,T_b,V_f_2,V_B_2))) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_subset__image__iff,axiom,
% 0.94/1.33 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] :
% 0.94/1.33 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)))
% 0.94/1.33 <=> ? [B_AA] :
% 0.94/1.33 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),B_AA),V_A_2))
% 0.94/1.33 & V_B_2 = c_Set_Oimage(T_b,T_a,V_f_2,B_AA) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_nat__case__Suc,axiom,
% 0.94/1.33 ! [V_nat_2,V_f2_2,V_f1_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_nat__case__0,axiom,
% 0.94/1.33 ! [V_f2_2,V_f1_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ).
% 0.94/1.33
% 0.94/1.33 fof(fact_finite__range__imageI,axiom,
% 0.94/1.33 ! [V_f_2,T_c,V_g_2,T_b,T_a] :
% 0.94/1.33 ( c_Finite__Set_Ofinite(T_a,c_Set_Oimage(T_b,T_a,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 0.94/1.33 => c_Finite__Set_Ofinite(T_c,c_Set_Oimage(T_b,T_c,hAPP(c_COMBB(T_a,T_c,T_b,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_pigeonhole,axiom,
% 0.94/1.33 ! [V_A_2,V_f_2,T_b,T_a] :
% 0.94/1.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))),c_Finite__Set_Ocard(T_b,V_A_2)))
% 0.94/1.33 => ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_inv__into__image__cancel,axiom,
% 0.94/1.33 ! [V_S_2,V_A_2,V_f_2,T_b,T_a] :
% 0.94/1.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 0.94/1.33 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_S_2),V_A_2))
% 0.94/1.33 => c_Set_Oimage(T_b,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,V_A_2,V_f_2),c_Set_Oimage(T_a,T_b,V_f_2,V_S_2)) = V_S_2 ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_inj__on__inv__into,axiom,
% 0.94/1.33 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] :
% 0.94/1.33 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2),c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)))
% 0.94/1.33 => c_Fun_Oinj__on(T_a,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_a,V_A_2,V_f_2),V_B_2) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_surj__imp__inj__inv,axiom,
% 0.94/1.33 ! [V_f_2,T_a,T_b] :
% 0.94/1.33 ( c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
% 0.94/1.33 => c_Fun_Oinj__on(T_a,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_a,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_inv__image__comp,axiom,
% 0.94/1.33 ! [V_X_2,V_f_2,T_b,T_a] :
% 0.94/1.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 0.94/1.33 => c_Set_Oimage(T_b,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),c_Set_Oimage(T_a,T_b,V_f_2,V_X_2)) = V_X_2 ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_image__inv__f__f,axiom,
% 0.94/1.33 ! [V_A_2,V_f_2,T_b,T_a] :
% 0.94/1.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 0.94/1.33 => c_Set_Oimage(T_b,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = V_A_2 ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_inj__imp__surj__inv,axiom,
% 0.94/1.33 ! [V_f_2,T_b,T_a] :
% 0.94/1.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 0.94/1.33 => c_Set_Oimage(T_b,T_a,c_Hilbert__Choice_Oinv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_funcset__image,axiom,
% 0.94/1.33 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 0.94/1.33 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,T_b)),V_f_2),c_FuncSet_OPi(T_a,T_b,V_A_2,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_B_2))))
% 0.94/1.33 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),V_B_2)) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_card__bij__eq,axiom,
% 0.94/1.33 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 0.94/1.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 0.94/1.33 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),V_B_2))
% 0.94/1.33 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2)
% 0.94/1.33 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_g_2,V_B_2)),V_A_2))
% 0.94/1.33 => ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 0.94/1.33 => ( c_Finite__Set_Ofinite(T_b,V_B_2)
% 0.94/1.33 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Finite__Set_Ocard(T_b,V_B_2) ) ) ) ) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_card__inj__on__le,axiom,
% 0.94/1.33 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 0.94/1.33 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 0.94/1.33 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),V_B_2))
% 0.94/1.33 => ( c_Finite__Set_Ofinite(T_b,V_B_2)
% 0.94/1.33 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_b,V_B_2))) ) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_1230_O_O_060N_125_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
% 0.94/1.33 ~ ! [B_h] :
% 0.94/1.33 ( c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,B_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))
% 0.94/1.33 => c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,B_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_inj__on__iff__card__le,axiom,
% 0.94/1.33 ! [V_B_2,T_b,V_A_2,T_a] :
% 0.94/1.33 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 0.94/1.33 => ( c_Finite__Set_Ofinite(T_b,V_B_2)
% 0.94/1.33 => ( ? [B_f] :
% 0.94/1.33 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2)
% 0.94/1.33 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,B_f,V_A_2)),V_B_2)) )
% 0.94/1.33 <=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2)),c_Finite__Set_Ocard(T_b,V_B_2))) ) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_finite__atLeastLessThan,axiom,
% 0.94/1.33 ! [V_u_2,V_l_2] : c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2,V_u_2)) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_image__Suc__atLeastLessThan,axiom,
% 0.94/1.33 ! [V_j_2,V_i_2] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2),hAPP(c_Nat_OSuc,V_j_2)) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_image__add__atLeastLessThan,axiom,
% 0.94/1.33 ! [V_j_2,V_i_2,V_k_2] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_finite__nat__set__iff__bounded,axiom,
% 0.94/1.33 ! [V_N_2] :
% 0.94/1.33 ( c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)
% 0.94/1.33 <=> ? [B_m] :
% 0.94/1.33 ! [B_x] :
% 0.94/1.33 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 0.94/1.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 0.94/1.33 ! [V_N_2] :
% 0.94/1.33 ( c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)
% 0.94/1.33 <=> ? [B_m] :
% 0.94/1.33 ! [B_x] :
% 0.94/1.33 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 0.94/1.33 => hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_x),B_m)) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_atLeastLessThan__eq__iff,axiom,
% 0.94/1.33 ! [V_da_2,V_ca_2,V_ba_2,V_aa_2,T_a] :
% 0.94/1.33 ( class_Orderings_Olinorder(T_a)
% 0.94/1.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2))
% 0.94/1.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_da_2))
% 0.94/1.33 => ( c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_aa_2,V_ba_2) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2,V_da_2)
% 0.94/1.33 <=> ( V_aa_2 = V_ca_2
% 0.94/1.33 & V_ba_2 = V_da_2 ) ) ) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 0.94/1.33 ! [V_da_2,V_ca_2,V_ba_2,V_aa_2,T_a] :
% 0.94/1.33 ( class_Orderings_Olinorder(T_a)
% 0.94/1.33 => ( c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_aa_2,V_ba_2) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2,V_da_2)
% 0.94/1.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2))
% 0.94/1.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_da_2))
% 0.94/1.33 => V_aa_2 = V_ca_2 ) ) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 0.94/1.33 ! [V_da_2,V_ca_2,V_ba_2,V_aa_2,T_a] :
% 0.94/1.33 ( class_Orderings_Olinorder(T_a)
% 0.94/1.33 => ( c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_aa_2,V_ba_2) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2,V_da_2)
% 0.94/1.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_aa_2),V_ba_2))
% 0.94/1.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_da_2))
% 0.94/1.33 => V_ba_2 = V_da_2 ) ) ) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_subset__card__intvl__is__intvl,axiom,
% 0.94/1.33 ! [V_k_2,V_A_2] :
% 0.94/1.33 ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),V_A_2),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),c_Finite__Set_Ocard(tc_Nat_Onat,V_A_2)))))
% 0.94/1.33 => V_A_2 = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),c_Finite__Set_Ocard(tc_Nat_Onat,V_A_2))) ) ).
% 0.94/1.33
% 0.94/1.33 fof(fact_atLeastLessThan__subset__iff,axiom,
% 0.94/1.33 ! [V_da_2,V_ca_2,V_ba_2,V_aa_2,T_a] :
% 0.94/1.33 ( class_Orderings_Olinorder(T_a)
% 0.94/1.33 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_aa_2,V_ba_2)),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2,V_da_2)))
% 0.94/1.33 => ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2),V_aa_2))
% 0.94/1.33 | ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2),V_aa_2))
% 0.94/1.33 & hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_ba_2),V_da_2)) ) ) ) ) ).
% 0.94/1.33
% 0.94/1.33 %----Arity declarations (33)
% 0.94/1.33 fof(arity_fun__Orderings_Opreorder,axiom,
% 0.94/1.33 ! [T_2,T_1] :
% 0.94/1.33 ( class_Orderings_Opreorder(T_1)
% 0.94/1.33 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 0.94/1.33 ! [T_1,T_2] :
% 0.94/1.33 ( ( class_Finite__Set_Ofinite(T_2)
% 0.94/1.33 & class_Finite__Set_Ofinite(T_1) )
% 0.94/1.33 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_fun__Orderings_Oorder,axiom,
% 0.94/1.33 ! [T_2,T_1] :
% 0.94/1.33 ( class_Orderings_Oorder(T_1)
% 0.94/1.33 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_fun__Orderings_Otop,axiom,
% 0.94/1.33 ! [T_2,T_1] :
% 0.94/1.33 ( class_Orderings_Otop(T_1)
% 0.94/1.33 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_fun__Orderings_Oord,axiom,
% 0.94/1.33 ! [T_2,T_1] :
% 0.94/1.33 ( class_Orderings_Oord(T_1)
% 0.94/1.33 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 0.94/1.33 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 0.94/1.33 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 0.94/1.33 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 0.94/1.33 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 0.94/1.33 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 0.94/1.33 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 0.94/1.33 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 0.94/1.33 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 0.94/1.33 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 0.94/1.33 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 0.94/1.33 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 0.94/1.33 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 0.94/1.33 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 0.94/1.33 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 0.94/1.33 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 0.94/1.33 class_Orderings_Oorder(tc_Nat_Onat) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 0.94/1.33 class_Orderings_Oord(tc_Nat_Onat) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 0.94/1.33 class_Groups_Ozero(tc_Nat_Onat) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 0.94/1.33 class_Groups_Oone(tc_Nat_Onat) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 0.94/1.33 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 0.94/1.33 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 0.94/1.33 class_Orderings_Oorder(tc_HOL_Obool) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 0.94/1.33 class_Orderings_Otop(tc_HOL_Obool) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 0.94/1.33 class_Orderings_Oord(tc_HOL_Obool) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 0.94/1.33 ! [T_1,T_2] :
% 0.94/1.33 ( ( class_Finite__Set_Ofinite(T_2)
% 0.94/1.33 & class_Finite__Set_Ofinite(T_1) )
% 0.94/1.33 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 0.94/1.33 ! [T_1] :
% 0.94/1.33 ( class_Finite__Set_Ofinite(T_1)
% 0.94/1.33 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 0.94/1.33 ! [T_1,T_2] :
% 0.94/1.33 ( ( class_Finite__Set_Ofinite(T_2)
% 0.94/1.33 & class_Finite__Set_Ofinite(T_1) )
% 0.94/1.33 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 0.94/1.33
% 0.94/1.33 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 0.94/1.33 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 0.94/1.33
% 0.94/1.33 %----Helper facts (8)
% 0.94/1.33 fof(help_c__COMBI__1,axiom,
% 0.94/1.33 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 0.94/1.33
% 0.94/1.33 fof(help_c__COMBK__1,axiom,
% 0.94/1.33 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 0.94/1.33
% 0.94/1.33 fof(help_c__COMBB__1,axiom,
% 0.94/1.33 ! [V_R_2,V_Q_2,V_Pa_2,T_c,T_a,T_b] : hAPP(hAPP(c_COMBB(T_b,T_a,T_c,V_Pa_2),V_Q_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Q_2,V_R_2)) ).
% 0.94/1.33
% 0.94/1.33 fof(help_c__COMBC__1,axiom,
% 0.94/1.33 ! [V_R_2,V_Q_2,V_Pa_2,T_a,T_c,T_b] : hAPP(hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_Pa_2),V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Q_2) ).
% 0.94/1.33
% 0.94/1.33 fof(help_c__COMBS__1,axiom,
% 0.94/1.33 ! [V_R_2,V_Q_2,V_Pa_2,T_a,T_c,T_b] : hAPP(c_COMBS(T_b,T_c,T_a,V_Pa_2,V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Q_2,V_R_2)) ).
% 0.94/1.33
% 0.94/1.33 fof(help_c__fequal__1,axiom,
% 0.94/1.33 ! [V_y_2,V_x_2] :
% 0.94/1.33 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 0.94/1.33 | V_x_2 = V_y_2 ) ).
% 0.94/1.33
% 0.94/1.33 fof(help_c__fequal__2,axiom,
% 0.94/1.33 ! [V_y_2,V_x_2] :
% 0.94/1.33 ( V_x_2 != V_y_2
% 0.94/1.33 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 0.94/1.33
% 0.94/1.33 fof(help_c__fFalse__1,axiom,
% 0.94/1.33 ~ hBOOL(c_fFalse) ).
% 0.94/1.33
% 0.94/1.33 %----Conjectures (1)
% 0.94/1.33 fof(conj_0,conjecture,
% 0.94/1.33 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_F,v_P____)))
% 0.94/1.33 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))) ) ).
% 0.94/1.33
% 0.94/1.33 %------------------------------------------------------------------------------
% 0.94/1.33 %-------------------------------------------
% 0.94/1.33 % Proof found
% 0.94/1.33 % SZS status Theorem for theBenchmark
% 0.94/1.33 % SZS output start Proof
% 0.94/1.33 %ClaNum:1030(EqnAxiom:275)
% 0.94/1.33 %VarNum:5452(SingletonVarNum:1765)
% 0.94/1.33 %MaxLitNum:10
% 0.94/1.33 %MaxfuncDepth:12
% 0.94/1.33 %SharedTerms:246
% 0.94/1.33 %goalClause: 1029 1030
% 0.94/1.33 [276]P1(a1)
% 0.94/1.33 [277]P2(a1)
% 0.94/1.33 [278]P4(a2)
% 0.94/1.33 [279]P5(a93)
% 0.94/1.33 [280]P5(a2)
% 0.94/1.33 [281]P6(a93)
% 0.94/1.33 [282]P28(a93)
% 0.94/1.33 [283]P28(a2)
% 0.94/1.33 [284]P29(a93)
% 0.94/1.33 [285]P29(a2)
% 0.94/1.33 [286]P30(a93)
% 0.94/1.33 [287]P7(a93)
% 0.94/1.33 [288]P8(a93)
% 0.94/1.33 [289]P9(a93)
% 0.94/1.33 [290]P10(a93)
% 0.94/1.33 [291]P11(a93)
% 0.94/1.33 [292]P20(a93)
% 0.94/1.33 [293]P24(a93)
% 0.94/1.33 [294]P12(a2)
% 0.94/1.33 [295]P12(a94)
% 0.94/1.33 [296]P25(a93)
% 1.10/1.33 [297]P21(a93)
% 1.10/1.33 [298]P22(a93)
% 1.10/1.33 [299]P33(a93)
% 1.10/1.33 [300]P26(a93)
% 1.10/1.33 [301]P31(a93)
% 1.10/1.33 [302]P35(a93)
% 1.10/1.33 [385]~E(a106,a105)
% 1.10/1.33 [386]~E(a103,a102)
% 1.10/1.33 [387]~P36(a39)
% 1.10/1.33 [303]E(f20(f3(a93)),f3(a93))
% 1.10/1.33 [305]E(f27(a21,f3(a93)),f4(a93))
% 1.10/1.33 [311]P13(a91,f30(f96(a91,a2)))
% 1.10/1.33 [342]P14(a91,a93,a99,f30(f96(a91,a2)))
% 1.10/1.33 [343]P14(a91,a93,a45,f30(f96(a91,a2)))
% 1.10/1.33 [312]E(f14(a94,f30(f96(a94,a2))),f4(a93))
% 1.10/1.33 [344]P36(f27(f27(f29(a93),a108),f14(a91,f30(f96(a91,a2)))))
% 1.10/1.33 [345]P36(f27(f27(f29(a93),a46),f14(a91,f30(f96(a91,a2)))))
% 1.10/1.33 [346]P36(f27(f27(f29(a93),a65),f14(a91,f30(f96(a91,a2)))))
% 1.10/1.33 [353]E(f31(a93,f3(a93),f14(a91,f30(f96(a91,a2)))),f36(a91,a93,a99,f30(f96(a91,a2))))
% 1.10/1.33 [354]E(f31(a93,f3(a93),f14(a91,f30(f96(a91,a2)))),f36(a91,a93,a45,f30(f96(a91,a2))))
% 1.10/1.33 [358]P36(f27(f27(f34(f96(f98(a92,a92),a2)),a100),a7))
% 1.10/1.33 [359]P36(f27(f27(f34(f96(f98(a92,a92),a2)),a101),a7))
% 1.10/1.33 [360]P36(f27(f27(f34(f96(f98(a92,a92),a2)),a47),a7))
% 1.10/1.33 [361]P36(f27(f27(f34(f96(f98(a92,a92),a2)),a64),a7))
% 1.10/1.33 [364]P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a102),a103)),a100))
% 1.10/1.33 [365]P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a102),a103)),a64))
% 1.10/1.33 [366]P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a103),a102)),a101))
% 1.10/1.33 [367]P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a103),a102)),a47))
% 1.10/1.33 [404]~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a102),a103)),a101))
% 1.10/1.33 [405]~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a103),a102)),a100))
% 1.10/1.33 [369]E(f17(a91,f96(f98(a92,a92),a2),f30(f96(a91,a2)),f27(f15(f96(f96(f98(a92,a92),a2),a2),a91),a7)),a8)
% 1.10/1.33 [372]P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),a104),a8))
% 1.10/1.33 [378]P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(a104,f27(f22(a91,a93,f30(f96(a91,a2)),a99),a108))))
% 1.10/1.33 [379]P36(f27(f27(f34(f96(f96(a91,f96(f98(a92,a92),a2)),f96(f98(a92,a92),a2))),a1),f17(f96(a91,f96(f98(a92,a92),a2)),f96(f98(a92,a92),a2),a8,f27(f15(f96(f96(f98(a92,a92),a2),a2),f96(a91,f96(f98(a92,a92),a2))),a7))))
% 1.10/1.33 [381]P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a103),a102)),f27(a1,f27(f27(f6(a91,f96(f98(a92,a92),a2),f96(f98(a92,a92),a2)),f27(f27(f6(a91,f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2))),f27(f9(a2,f96(f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2))),a91,f23(f96(f98(a92,a92),a2))),f27(f27(f6(a91,a93,a2),f27(f9(a93,f96(a93,a2),a91,f29(a93)),a99)),f27(f27(f19(a93),a108),f4(a93))))),a101)),a100))))
% 1.10/1.33 [382]P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a103),a102)),f27(a1,f27(f27(f6(a91,f96(f98(a92,a92),a2),f96(f98(a92,a92),a2)),f27(f27(f6(a91,f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2))),f27(f9(a2,f96(f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2))),a91,f23(f96(f98(a92,a92),a2))),f27(f27(f6(a91,a93,a2),f27(f9(a93,f96(a93,a2),a91,f29(a93)),a99)),f27(f27(f19(a93),a46),f4(a93))))),a101)),a100))))
% 1.10/1.33 [383]P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a103),a102)),f27(a1,f27(f27(f6(a91,f96(f98(a92,a92),a2),f96(f98(a92,a92),a2)),f27(f27(f6(a91,f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2))),f27(f9(a2,f96(f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2))),a91,f23(f96(f98(a92,a92),a2))),f27(f27(f6(a91,a93,a2),f27(f9(a93,f96(a93,a2),a91,f29(a93)),a99)),f27(f27(f19(a93),a65),f4(a93))))),a101)),a100))))
% 1.10/1.33 [384]P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),f16(a91,f96(f98(a92,a92),a2),f96(f98(a92,a92),a2),f16(a91,f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2)),f27(f9(a2,f96(f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2))),a91,f23(f96(f98(a92,a92),a2))),f27(f27(f6(a91,a93,a2),f27(f9(a93,f96(a93,a2),a91,f29(a93)),a99)),a108)),f27(f27(f6(a91,a92,f96(f98(a92,a92),a2)),f27(f9(f96(f98(a92,a92),a2),f96(a92,f96(f98(a92,a92),a2)),a91,a10),a104)),a107)),f16(a91,f96(f98(a92,a92),a2),f96(f98(a92,a92),a2),f16(a91,f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2)),f27(f9(a2,f96(f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2))),a91,f23(f96(f98(a92,a92),a2))),f27(f27(f6(a91,a93,a2),f27(f9(a93,f96(a93,a2),a91,a38),a99)),a108)),f27(f27(f6(a91,a92,f96(f98(a92,a92),a2)),f27(f27(f6(a91,a92,f96(a92,f96(f98(a92,a92),a2))),f27(f9(f96(f98(a92,a92),a2),f96(a92,f96(a92,f96(f98(a92,a92),a2))),a91,a11),a104)),a105)),a107)),f27(f27(f6(a91,a92,f96(f98(a92,a92),a2)),f27(f9(f96(f98(a92,a92),a2),f96(a92,f96(f98(a92,a92),a2)),a91,a12),a104)),a107)))),a8))
% 1.10/1.33 [333]P14(a93,a93,a21,x3331)
% 1.10/1.33 [304]E(f26(a93,x3041),x3041)
% 1.10/1.33 [389]~E(f27(a21,x3891),x3891)
% 1.10/1.33 [395]~E(f27(a21,x3951),f3(a93))
% 1.10/1.33 [308]E(f27(f27(f19(a93),x3081),f3(a93)),x3081)
% 1.10/1.33 [309]E(f28(a93,f27(a21,x3091)),f27(f29(a93),x3091))
% 1.10/1.33 [313]E(f27(f27(f19(a93),x3131),f4(a93)),f27(a21,x3131))
% 1.10/1.33 [315]P36(f27(f28(a93,x3151),x3151))
% 1.10/1.33 [323]P36(f27(f27(f29(a93),x3231),f27(a21,x3231)))
% 1.10/1.33 [324]P36(f27(f27(f29(a93),f3(a93)),f27(a21,x3241)))
% 1.10/1.33 [400]~P36(f27(f27(f29(a93),x4001),f3(a93)))
% 1.10/1.33 [310]E(f27(f27(f19(a93),f3(a93)),x3101),x3101)
% 1.10/1.33 [314]E(f27(f27(f19(a93),f4(a93)),x3141),f27(a21,x3141))
% 1.10/1.33 [317]P36(f27(f28(a93,f3(a93)),x3171))
% 1.10/1.33 [320]E(f27(f27(f19(a93),f20(x3201)),f27(a21,f3(a93))),f20(f27(a21,x3201)))
% 1.10/1.33 [325]E(f27(f27(f19(a93),f26(a93,x3251)),f27(a21,f3(a93))),f26(a93,f27(a21,x3251)))
% 1.10/1.33 [397]~P36(f27(f27(f29(a93),x3971),x3971))
% 1.10/1.33 [401]~P36(f27(f28(a93,f27(a21,x4011)),x4011))
% 1.10/1.33 [380]P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),f27(f27(f6(a91,f96(f98(a92,a92),a2),f96(f98(a92,a92),a2)),f27(f27(f6(a91,f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2))),f27(f9(a2,f96(f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2))),a91,f23(f96(f98(a92,a92),a2))),f27(f27(f6(a91,a93,a2),f27(f9(a93,f96(a93,a2),a91,f29(a93)),a99)),x3801))),a101)),a100)),a8))
% 1.10/1.33 [321]P13(a93,f31(a93,x3211,x3212))
% 1.10/1.33 [335]P14(x3351,x3351,f5(x3351),x3352)
% 1.10/1.33 [307]E(f27(f5(x3071),x3072),x3072)
% 1.10/1.33 [336]E(f36(x3361,x3361,f5(x3361),x3362),x3362)
% 1.10/1.33 [352]E(f36(a93,a93,a21,f31(a93,x3521,x3522)),f31(a93,f27(a21,x3521),f27(a21,x3522)))
% 1.10/1.33 [318]E(f27(f27(f19(a93),x3181),x3182),f27(f27(f19(a93),x3182),x3181))
% 1.10/1.33 [322]P36(f27(f30(f96(x3221,a2)),x3222))
% 1.10/1.33 [326]E(f27(f27(f19(a93),f27(a21,x3261)),x3262),f27(f27(f19(a93),x3261),f27(a21,x3262)))
% 1.10/1.33 [328]P36(f27(f28(f96(x3281,a2),x3282),x3282))
% 1.10/1.33 [331]P36(f27(f27(f34(x3311),x3312),f30(f96(x3311,a2))))
% 1.10/1.33 [340]P36(f27(f28(f96(x3401,a2),x3402),f30(f96(x3401,a2))))
% 1.10/1.33 [351]E(f37(x3511,x3512,f30(f96(x3511,a2)),f30(f96(x3512,a2))),f30(f96(f97(x3511,x3512),a2)))
% 1.10/1.33 [363]P14(a93,a93,f27(f27(f6(a93,a93,a93),f19(a93)),x3631),x3632)
% 1.10/1.33 [327]E(f27(f27(f19(a93),x3271),f27(a21,x3272)),f27(a21,f27(f27(f19(a93),x3271),x3272)))
% 1.10/1.33 [329]E(f27(f27(f19(a93),f27(a21,x3291)),x3292),f27(a21,f27(f27(f19(a93),x3291),x3292)))
% 1.10/1.33 [337]P36(f27(f28(a93,x3371),f27(f27(f19(a93),x3372),x3371)))
% 1.10/1.33 [338]P36(f27(f28(a93,x3381),f27(f27(f19(a93),x3381),x3382)))
% 1.10/1.33 [355]P36(f27(f27(f29(a93),x3551),f27(a21,f27(f27(f19(a93),x3552),x3551))))
% 1.10/1.33 [356]P36(f27(f27(f29(a93),x3561),f27(a21,f27(f27(f19(a93),x3561),x3562))))
% 1.10/1.33 [375]P36(f27(f27(f34(f96(x3751,x3751)),f5(x3751)),f17(x3751,x3751,x3752,f27(f15(f96(x3751,a2),x3751),x3752))))
% 1.10/1.33 [402]~P36(f27(f27(f29(a93),f27(f27(f19(a93),x4021),x4022)),x4022))
% 1.10/1.33 [403]~P36(f27(f27(f29(a93),f27(f27(f19(a93),x4031),x4032)),x4031))
% 1.10/1.33 [332]E(f35(x3321,x3322,f35(x3321,x3322,x3323)),f35(x3321,x3322,x3323))
% 1.10/1.33 [334]E(f25(x3341,x3342,x3343,f3(a93)),x3342)
% 1.10/1.33 [347]P36(f27(f27(f34(x3471),x3472),f35(x3471,x3472,x3473)))
% 1.10/1.33 [350]P36(f27(f28(f96(x3501,a2),x3502),f35(x3501,x3503,x3502)))
% 1.10/1.33 [339]E(f27(f27(f19(a93),x3391),f27(f27(f19(a93),x3392),x3393)),f27(f27(f19(a93),x3392),f27(f27(f19(a93),x3391),x3393)))
% 1.10/1.33 [362]E(f17(x3621,x3622,x3623,f27(f15(f96(x3622,a2),x3621),f30(f96(x3622,a2)))),f30(f96(f96(x3621,x3622),a2)))
% 1.10/1.33 [370]E(f36(a93,a93,f27(f27(f6(a93,a93,a93),f19(a93)),x3701),f31(a93,x3702,x3703)),f31(a93,f27(f27(f19(a93),x3702),x3701),f27(f27(f19(a93),x3703),x3701)))
% 1.10/1.33 [349]E(f27(f27(f19(a93),f27(f27(f19(a93),x3491),x3492)),x3493),f27(f27(f19(a93),x3491),f27(f27(f19(a93),x3492),x3493)))
% 1.10/1.33 [341]E(f25(x3411,x3412,x3413,f27(a21,x3414)),f27(x3413,x3414))
% 1.10/1.33 [348]E(f35(x3481,x3482,f35(x3481,x3483,x3484)),f35(x3481,x3483,f35(x3481,x3482,x3484)))
% 1.10/1.33 [319]E(f27(f27(f15(x3191,x3192),x3193),x3194),x3193)
% 1.10/1.33 [373]P36(f27(f27(f34(x3731),f27(x3732,x3733)),f36(x3734,x3731,x3732,f30(f96(x3734,a2)))))
% 1.10/1.33 [368]E(f36(x3681,x3682,x3683,f35(x3681,x3684,x3685)),f35(x3682,f27(x3683,x3684),f36(x3681,x3682,x3683,x3685)))
% 1.10/1.33 [376]E(f36(x3761,x3762,f27(f9(x3763,x3762,x3761,x3764),x3765),f30(f96(x3761,a2))),f36(x3763,x3762,x3764,f36(x3761,x3763,x3765,f30(f96(x3761,a2)))))
% 1.10/1.33 [377]E(f27(f16(x3771,x3772,x3773,x3774,x3775),x3776),f27(f27(x3774,x3776),f27(x3775,x3776)))
% 1.10/1.33 [371]E(f27(f27(f9(x3711,x3712,x3713,x3714),x3715),x3716),f27(x3714,f27(x3715,x3716)))
% 1.10/1.33 [374]E(f36(x3741,x3742,x3743,f36(x3744,x3741,x3745,x3746)),f36(x3744,x3742,f27(f9(x3741,x3742,x3744,x3743),x3745),x3746))
% 1.10/1.33 [357]E(f27(f27(f27(f6(x3571,x3572,x3573),x3574),x3575),x3576),f27(f27(x3574,x3576),x3575))
% 1.10/1.33 [1029]P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(a1,a104)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(a1,f16(a91,f96(f98(a92,a92),a2),f96(f98(a92,a92),a2),f16(a91,f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2)),f27(f9(a2,f96(f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2))),a91,f23(f96(f98(a92,a92),a2))),f27(f27(f6(a91,a93,a2),f27(f9(a93,f96(a93,a2),a91,f29(a93)),a99)),a108)),f27(f27(f6(a91,a92,f96(f98(a92,a92),a2)),f27(f9(f96(f98(a92,a92),a2),f96(a92,f96(f98(a92,a92),a2)),a91,a10),a104)),a107)),f16(a91,f96(f98(a92,a92),a2),f96(f98(a92,a92),a2),f16(a91,f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2)),f27(f9(a2,f96(f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2))),a91,f23(f96(f98(a92,a92),a2))),f27(f27(f6(a91,a93,a2),f27(f9(a93,f96(a93,a2),a91,a38),a99)),a108)),f27(f27(f6(a91,a92,f96(f98(a92,a92),a2)),f27(f27(f6(a91,a92,f96(a92,f96(f98(a92,a92),a2))),f27(f9(f96(f98(a92,a92),a2),f96(a92,f96(a92,f96(f98(a92,a92),a2))),a91,a11),a104)),a105)),a107)),f27(f27(f6(a91,a92,f96(f98(a92,a92),a2)),f27(f9(f96(f98(a92,a92),a2),f96(a92,f96(f98(a92,a92),a2)),a91,a12),a104)),a107))))))
% 1.10/1.33 [1030]~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(a1,a104)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(a1,f16(a91,f96(f98(a92,a92),a2),f96(f98(a92,a92),a2),f16(a91,f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2)),f27(f9(a2,f96(f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2))),a91,f23(f96(f98(a92,a92),a2))),f27(f27(f6(a91,a93,a2),f27(f9(a93,f96(a93,a2),a91,f29(a93)),a99)),a108)),f27(f27(f6(a91,a92,f96(f98(a92,a92),a2)),f27(f9(f96(f98(a92,a92),a2),f96(a92,f96(f98(a92,a92),a2)),a91,a10),a104)),a107)),f16(a91,f96(f98(a92,a92),a2),f96(f98(a92,a92),a2),f16(a91,f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2)),f27(f9(a2,f96(f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2))),a91,f23(f96(f98(a92,a92),a2))),f27(f27(f6(a91,a93,a2),f27(f9(a93,f96(a93,a2),a91,a38),a99)),a108)),f27(f27(f6(a91,a92,f96(f98(a92,a92),a2)),f27(f27(f6(a91,a92,f96(a92,f96(f98(a92,a92),a2))),f27(f9(f96(f98(a92,a92),a2),f96(a92,f96(a92,f96(f98(a92,a92),a2))),a91,a11),a104)),a105)),a107)),f27(f27(f6(a91,a92,f96(f98(a92,a92),a2)),f27(f9(f96(f98(a92,a92),a2),f96(a92,f96(f98(a92,a92),a2)),a91,a12),a104)),a107))))))
% 1.10/1.33 [406]~P12(x4061)+P12(f95(x4061))
% 1.10/1.33 [408]~P33(x4081)+~E(f4(x4081),f3(x4081))
% 1.10/1.33 [465]~P30(x4651)+P36(f27(f28(x4651,f3(x4651)),f4(x4651)))
% 1.10/1.33 [470]E(x4701,f3(a93))+~P36(f27(f28(a93,x4701),f3(a93)))
% 1.10/1.33 [479]~P34(x4791)+P36(f27(f27(f34(x4791),f4(x4791)),f24(x4791)))
% 1.10/1.33 [480]~P34(x4801)+P36(f27(f27(f34(x4801),f3(x4801)),f24(x4801)))
% 1.10/1.33 [481]~P30(x4811)+P36(f27(f27(f29(x4811),f3(x4811)),f4(x4811)))
% 1.10/1.33 [520]~P30(x5201)+~P36(f27(f28(x5201,f4(x5201)),f3(x5201)))
% 1.10/1.33 [549]~P30(x5491)+~P36(f27(f27(f29(x5491),f4(x5491)),f3(x5491)))
% 1.10/1.33 [458]E(x4581,f3(a93))+P36(f27(f27(f29(a93),f3(a93)),x4581))
% 1.10/1.33 [516]E(f27(a21,f67(x5161)),x5161)+~P36(f27(f27(f29(a93),f3(a93)),x5161))
% 1.10/1.33 [528]~P13(x5281,f30(f96(x5281,a2)))+P13(f95(x5281),f30(f96(f95(x5281),a2)))
% 1.10/1.33 [535]P13(x5351,f30(f96(x5351,a2)))+~P13(f95(x5351),f30(f96(f95(x5351),a2)))
% 1.10/1.33 [556]E(x5561,f3(a93))+~P36(f27(f27(f29(a93),x5561),f27(a21,f3(a93))))
% 1.10/1.33 [662]~P30(x6621)+P36(f27(f27(f29(x6621),f3(x6621)),f27(f27(f19(x6621),f4(x6621)),f4(x6621))))
% 1.10/1.33 [836]P1(x8361)+P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),f51(x8361)),a8))
% 1.10/1.33 [837]P1(x8371)+P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),f52(x8371)),a8))
% 1.10/1.33 [838]P2(x8381)+P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),f50(x8381)),a8))
% 1.10/1.33 [855]P2(x8551)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),f49(x8551)),f56(x8551))),f27(x8551,f50(x8551))))
% 1.10/1.33 [683]~P13(x6831,f30(f96(x6831,a2)))+P36(f27(f27(f29(a93),f3(a93)),f14(x6831,f30(f96(x6831,a2)))))
% 1.10/1.33 [915]~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9151),a7))+P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),f27(f15(f96(f98(a92,a92),a2),a91),x9151)),a8))
% 1.10/1.33 [1026]~P36(f27(f28(a93,x10261),a108))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a102),a103)),f27(a1,f27(f27(f6(a91,f96(f98(a92,a92),a2),f96(f98(a92,a92),a2)),f27(f27(f6(a91,f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2))),f27(f9(a2,f96(f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2))),a91,f23(f96(f98(a92,a92),a2))),f27(f27(f6(a91,a93,a2),f27(f9(a93,f96(a93,a2),a91,f29(a93)),a99)),x10261))),a101)),a100))))
% 1.10/1.33 [1027]~P36(f27(f28(a93,x10271),a46))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a102),a103)),f27(a1,f27(f27(f6(a91,f96(f98(a92,a92),a2),f96(f98(a92,a92),a2)),f27(f27(f6(a91,f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2))),f27(f9(a2,f96(f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2))),a91,f23(f96(f98(a92,a92),a2))),f27(f27(f6(a91,a93,a2),f27(f9(a93,f96(a93,a2),a91,f29(a93)),a99)),x10271))),a101)),a100))))
% 1.10/1.33 [1028]~P36(f27(f28(a93,x10281),a65))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a102),a103)),f27(a1,f27(f27(f6(a91,f96(f98(a92,a92),a2),f96(f98(a92,a92),a2)),f27(f27(f6(a91,f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2))),f27(f9(a2,f96(f96(f98(a92,a92),a2),f96(f96(f98(a92,a92),a2),f96(f98(a92,a92),a2))),a91,f23(f96(f98(a92,a92),a2))),f27(f27(f6(a91,a93,a2),f27(f9(a93,f96(a93,a2),a91,f29(a93)),a99)),x10281))),a101)),a100))))
% 1.10/1.33 [410]~P12(x4101)+P13(x4101,x4102)
% 1.10/1.33 [412]P13(x4121,x4122)+E(f14(x4121,x4122),f3(a93))
% 1.10/1.33 [413]~P4(x4132)+P4(f96(x4131,x4132))
% 1.10/1.33 [414]~P5(x4142)+P5(f96(x4141,x4142))
% 1.10/1.33 [415]~P28(x4152)+P28(f96(x4151,x4152))
% 1.10/1.33 [416]~P29(x4162)+P29(f96(x4161,x4162))
% 1.10/1.33 [418]E(x4181,x4182)+~E(f27(a21,x4181),f27(a21,x4182))
% 1.10/1.33 [423]~P21(x4231)+E(f27(f27(f19(x4231),x4232),f3(x4231)),x4232)
% 1.10/1.33 [424]~P22(x4241)+E(f27(f27(f19(x4241),x4242),f3(x4241)),x4242)
% 1.10/1.33 [425]~P31(x4251)+E(f27(f27(f19(x4251),x4252),f3(x4251)),x4252)
% 1.10/1.33 [434]~E(x4341,x4342)+P36(f27(f27(a38,x4341),x4342))
% 1.10/1.33 [437]~E(x4371,x4372)+P36(f27(f28(a93,x4371),x4372))
% 1.10/1.33 [442]~P5(x4421)+P36(f27(f28(x4421,x4422),x4422))
% 1.10/1.33 [454]~P4(x4541)+P36(f27(f28(x4541,x4542),f30(x4541)))
% 1.10/1.33 [464]E(x4641,x4642)+~P36(f27(f27(a38,x4641),x4642))
% 1.10/1.33 [466]E(x4661,x4662)+~E(f27(x4661,f48(x4662,x4661)),f27(x4662,f48(x4662,x4661)))
% 1.10/1.33 [471]P3(x4711,x4712)+~E(f27(x4711,f59(x4712,x4711)),f27(f59(x4712,x4711),x4712))
% 1.10/1.33 [473]~E(x4731,x4732)+P36(f27(f27(f29(a93),x4731),f27(a21,x4732)))
% 1.10/1.33 [476]~E(x4761,f3(a93))+P36(f27(f27(f29(a93),x4761),f27(a21,x4762)))
% 1.10/1.33 [488]P36(f27(f28(a93,x4882),x4881))+P36(f27(f28(a93,x4881),x4882))
% 1.10/1.33 [519]E(f27(f27(f19(a93),x5191),f66(x5192,x5191)),x5192)+~P36(f27(f28(a93,x5191),x5192))
% 1.10/1.33 [553]~P36(f27(f28(a93,x5531),x5532))+P36(f27(f28(a93,x5531),f27(a21,x5532)))
% 1.10/1.33 [577]~P36(f27(f28(a93,x5771),x5772))+P36(f27(f27(f29(a93),x5771),f27(a21,x5772)))
% 1.10/1.33 [578]P13(x5781,x5782)+~P36(f27(f27(f29(a93),f3(a93)),f14(x5781,x5782)))
% 1.10/1.33 [597]P36(f27(f28(a93,x5971),x5972))+~P36(f27(f27(f29(a93),x5971),f27(a21,x5972)))
% 1.10/1.33 [622]~P36(f27(f28(a93,x6221),x6222))+P36(f27(f28(a93,f27(a21,x6221)),f27(a21,x6222)))
% 1.10/1.33 [661]P36(f27(f28(a93,x6611),x6612))+~P36(f27(f28(a93,f27(a21,x6611)),f27(a21,x6612)))
% 1.10/1.33 [964]~P13(x9641,x9642)+E(f18(a93,x9641,f19(a93),f27(f15(a93,x9641),f4(a93)),f3(a93),x9642),f14(x9641,x9642))
% 1.10/1.33 [429]~P21(x4291)+E(f27(f27(f19(x4291),f3(x4291)),x4292),x4292)
% 1.10/1.33 [430]~P22(x4301)+E(f27(f27(f19(x4301),f3(x4301)),x4302),x4302)
% 1.10/1.33 [431]~P31(x4311)+E(f27(f27(f19(x4311),f3(x4311)),x4312),x4312)
% 1.10/1.33 [433]E(x4331,f3(a93))+~E(f27(f27(f19(a93),x4332),x4331),x4332)
% 1.10/1.33 [438]E(x4381,f3(a93))+~E(f27(f27(f19(a93),x4382),x4381),f3(a93))
% 1.10/1.33 [439]E(x4391,f3(a93))+~E(f27(f27(f19(a93),x4391),x4392),f3(a93))
% 1.10/1.33 [467]~E(x4671,f27(a21,x4672))+P36(f27(f27(f29(a93),f3(a93)),x4671))
% 1.10/1.33 [487]~E(x4871,x4872)+~P36(f27(f27(f29(a93),x4871),x4872))
% 1.10/1.33 [489]~E(x4891,f3(a93))+~P36(f27(f27(f29(a93),x4892),x4891))
% 1.10/1.33 [501]~P5(x5011)+~P36(f27(f27(f29(x5011),x5012),x5012))
% 1.10/1.33 [530]P13(a93,x5301)+P36(f27(f27(f34(a93),f80(x5301,x5302)),x5301))
% 1.10/1.33 [531]P13(a93,x5311)+P36(f27(f27(f34(a93),f83(x5311,x5312)),x5311))
% 1.10/1.33 [548]P36(f27(f28(a93,x5481),x5482))+~P36(f27(f27(f29(a93),x5481),x5482))
% 1.10/1.33 [550]P36(f27(f27(f29(a93),x5502),f27(a21,x5501)))+P36(f27(f27(f29(a93),x5501),x5502))
% 1.10/1.33 [557]P36(f27(f28(a93,x5571),x5572))+P36(f27(f28(a93,f27(a21,x5572)),x5571))
% 1.10/1.33 [592]P36(f27(f27(f29(a93),x5921),f27(a21,x5922)))+~P36(f27(f27(f29(a93),x5921),x5922))
% 1.10/1.33 [596]P13(a93,x5961)+~P36(f27(f28(a93,f83(x5961,x5962)),x5962))
% 1.10/1.33 [598]E(f27(a21,f27(f27(f19(a93),x5981),f73(x5982,x5981))),x5982)+~P36(f27(f27(f29(a93),x5981),x5982))
% 1.10/1.33 [611]~P36(f27(f27(f29(a93),x6111),x6112))+P36(f27(f28(a93,f27(a21,x6111)),x6112))
% 1.10/1.33 [618]P13(a93,x6181)+~P36(f27(f27(f29(a93),f80(x6181,x6182)),x6182))
% 1.10/1.33 [624]P36(f27(f28(a93,x6241),x6242))+~P36(f27(f28(a93,f27(a21,x6241)),x6242))
% 1.10/1.33 [626]~P30(x6261)+P36(f27(f27(f29(x6261),x6262),f27(f27(f19(x6261),x6262),f4(x6261))))
% 1.10/1.33 [640]P36(f27(f27(f29(a93),x6401),x6402))+~P36(f27(f28(a93,f27(a21,x6401)),x6402))
% 1.10/1.33 [641]~P36(f27(f27(f29(a93),x6412),f27(a21,x6411)))+~P36(f27(f27(f29(a93),x6411),x6412))
% 1.10/1.33 [642]P13(x6421,f30(f96(x6421,a2)))+~P13(f96(x6422,x6421),f30(f96(f96(x6422,x6421),a2)))
% 1.10/1.33 [643]P13(x6431,f30(f96(x6431,a2)))+~P13(f97(x6432,x6431),f30(f96(f97(x6432,x6431),a2)))
% 1.10/1.33 [644]P13(x6441,f30(f96(x6441,a2)))+~P13(f97(x6441,x6442),f30(f96(f97(x6441,x6442),a2)))
% 1.10/1.34 [650]P36(f27(f27(f29(a93),f27(a21,x6501)),f27(a21,x6502)))+~P36(f27(f27(f29(a93),x6501),x6502))
% 1.10/1.34 [651]~P36(f27(f28(a93,x6511),x6512))+~P36(f27(f28(a93,f27(a21,x6512)),x6511))
% 1.10/1.34 [652]P36(f27(f27(f29(a93),x6521),x6522))+~P36(f27(f27(f29(a93),f27(a21,x6521)),x6522))
% 1.10/1.34 [681]~P36(f27(f27(f29(a93),f27(a21,x6811)),f27(a21,x6812)))+P36(f27(f27(f29(a93),x6811),x6812))
% 1.10/1.34 [763]P36(f25(a2,a39,f28(a93,x7631),x7632))+~P36(f27(f28(a93,f27(a21,x7631)),x7632))
% 1.10/1.34 [796]~P36(f25(a2,a39,f28(a93,x7961),x7962))+P36(f27(f28(a93,f27(a21,x7961)),x7962))
% 1.10/1.34 [819]P2(x8191)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),f49(x8191)),f56(x8191))),f27(f50(x8191),x8192)))
% 1.10/1.34 [842]P3(x8421,x8422)+P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),f59(x8422,x8421)),a8))
% 1.10/1.34 [847]E(f31(a93,x8471,f27(f27(f19(a93),x8471),f14(a93,x8472))),x8472)+~P36(f27(f28(f96(a93,a2),x8472),f31(a93,x8471,f27(f27(f19(a93),x8471),f14(a93,x8472)))))
% 1.10/1.34 [888]P18(x8881,x8882)+~P36(f27(f27(f34(f98(x8881,x8881)),f27(f27(f32(x8881,x8881),f78(x8882,x8881)),f78(x8882,x8881))),x8882))
% 1.10/1.34 [860]P36(f27(f27(f34(f96(f98(a92,a92),a2)),f27(f27(a10,x8601),x8602)),a7))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x8601),a7))
% 1.10/1.34 [861]P36(f27(f27(f34(f96(f98(a92,a92),a2)),f27(f27(a12,x8611),x8612)),a7))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x8611),a7))
% 1.10/1.34 [475]~P13(x4751,x4753)+P13(x4751,f35(x4751,x4752,x4753))
% 1.10/1.34 [529]P13(x5291,x5292)+~P13(x5291,f35(x5291,x5293,x5292))
% 1.10/1.34 [491]~E(x4912,x4913)+P36(f27(f27(f34(x4911),x4912),f27(a38,x4913)))
% 1.10/1.34 [554]E(x5541,x5542)+~P36(f27(f27(f34(x5543),x5541),f27(a38,x5542)))
% 1.10/1.34 [956]P13(x9561,x9562)+~P36(f27(f27(f34(f98(f96(x9561,a2),f96(x9561,a2))),f27(f27(f32(f96(x9561,a2),f96(x9561,a2)),x9563),x9562)),f41(x9561)))
% 1.10/1.34 [440]~P4(x4402)+E(f27(f30(f96(x4401,x4402)),x4403),f30(x4402))
% 1.10/1.34 [459]~P31(x4591)+E(f27(f27(f19(x4591),x4592),x4593),f27(f27(f19(x4591),x4593),x4592))
% 1.10/1.34 [477]E(x4771,x4772)+~E(f27(f27(f19(a93),x4773),x4771),f27(f27(f19(a93),x4773),x4772))
% 1.10/1.34 [478]E(x4781,x4782)+~E(f27(f27(f19(a93),x4781),x4783),f27(f27(f19(a93),x4782),x4783))
% 1.10/1.34 [482]~E(x4822,f27(f27(f19(a93),x4821),x4823))+P36(f27(f28(a93,x4821),x4822))
% 1.10/1.34 [490]~P36(f27(x4903,x4902))+P36(f27(f27(f34(x4901),x4902),x4903))
% 1.10/1.34 [502]~E(x5023,x5022)+P36(f27(f28(f96(x5021,a2),x5022),x5023))
% 1.10/1.34 [508]~E(x5082,x5083)+P36(f27(f28(f96(x5081,a2),x5082),x5083))
% 1.10/1.34 [526]P36(f27(x5261,x5262))+~P36(f27(f27(f34(x5263),x5262),x5261))
% 1.10/1.34 [543]E(f35(x5431,x5432,x5433),x5433)+~P36(f27(f27(f34(x5431),x5432),x5433))
% 1.10/1.34 [732]~P13(x7321,x7322)+P36(f27(f28(a93,f14(x7321,x7322)),f14(x7321,f35(x7321,x7323,x7322))))
% 1.10/1.34 [815]E(x8151,x8152)+~E(f27(f27(f6(x8153,f96(x8153,a2),a2),f34(x8153)),x8151),f27(f27(f6(x8153,f96(x8153,a2),a2),f34(x8153)),x8152))
% 1.10/1.34 [841]~P14(x8412,x8411,x8413,f30(f96(x8412,a2)))+E(f36(x8411,x8412,f22(x8412,x8411,f30(f96(x8412,a2)),x8413),f30(f96(x8411,a2))),f30(f96(x8412,a2)))
% 1.10/1.34 [843]P14(x8431,x8432,f22(x8432,x8431,f30(f96(x8432,a2)),x8433),f30(f96(x8431,a2)))+~E(f36(x8432,x8431,x8433,f30(f96(x8432,a2))),f30(f96(x8431,a2)))
% 1.10/1.34 [889]~E(f27(x8893,f27(f22(x8891,x8892,f30(f96(x8891,a2)),x8893),f75(x8893,x8892,x8891))),f75(x8893,x8892,x8891))+E(f36(x8891,x8892,x8893,f30(f96(x8891,a2))),f30(f96(x8892,a2)))
% 1.10/1.34 [573]~E(x5732,f27(a21,f27(f27(f19(a93),x5731),x5733)))+P36(f27(f27(f29(a93),x5731),x5732))
% 1.10/1.34 [646]~P36(f27(f28(a93,x6461),x6463))+P36(f27(f28(a93,x6461),f27(f27(f19(a93),x6462),x6463)))
% 1.10/1.34 [648]~P36(f27(f28(a93,x6481),x6482))+P36(f27(f28(a93,x6481),f27(f27(f19(a93),x6482),x6483)))
% 1.10/1.34 [670]~P36(f27(f27(f29(a93),x6701),x6703))+P36(f27(f27(f29(a93),x6701),f27(f27(f19(a93),x6702),x6703)))
% 1.10/1.34 [672]~P36(f27(f27(f29(a93),x6721),x6722))+P36(f27(f27(f29(a93),x6721),f27(f27(f19(a93),x6722),x6723)))
% 1.10/1.34 [682]~E(x6821,x6822)+~P36(f27(f27(f29(f96(x6823,a2)),x6821),x6822))
% 1.10/1.34 [722]P36(f27(f28(f96(x7221,a2),x7222),x7223))+~P36(f27(f27(f29(f96(x7221,a2)),x7222),x7223))
% 1.10/1.34 [745]~P36(f27(f28(a93,x7452),x7453))+P36(f27(f28(a93,f27(f27(f19(a93),x7451),x7452)),f27(f27(f19(a93),x7451),x7453)))
% 1.10/1.34 [746]~P36(f27(f28(a93,x7461),x7463))+P36(f27(f28(a93,f27(f27(f19(a93),x7461),x7462)),f27(f27(f19(a93),x7463),x7462)))
% 1.10/1.34 [757]~P36(f27(f27(f29(a93),x7572),x7573))+P36(f27(f27(f29(a93),f27(f27(f19(a93),x7571),x7572)),f27(f27(f19(a93),x7571),x7573)))
% 1.10/1.34 [758]~P36(f27(f27(f29(a93),x7581),x7583))+P36(f27(f27(f29(a93),f27(f27(f19(a93),x7581),x7582)),f27(f27(f19(a93),x7583),x7582)))
% 1.10/1.34 [803]P36(f27(f28(a93,x8031),x8032))+~P36(f27(f28(a93,f27(f27(f19(a93),x8033),x8031)),f27(f27(f19(a93),x8033),x8032)))
% 1.10/1.34 [814]P36(f27(f27(f29(a93),x8141),x8142))+~P36(f27(f27(f29(a93),f27(f27(f19(a93),x8143),x8141)),f27(f27(f19(a93),x8143),x8142)))
% 1.10/1.34 [946]~P36(f27(f28(f96(x9461,a2),x9462),x9463))+P36(f27(f28(f96(x9461,a2),f27(f27(f6(x9461,f96(x9461,a2),a2),f34(x9461)),x9462)),f27(f27(f6(x9461,f96(x9461,a2),a2),f34(x9461)),x9463)))
% 1.10/1.34 [960]~P36(f27(f27(f34(f98(f96(x9601,a2),f96(x9601,a2))),f27(f27(f32(f96(x9601,a2),f96(x9601,a2)),x9602),x9603)),f41(x9601)))+P36(f27(f27(f29(f96(x9601,a2)),x9602),x9603))
% 1.10/1.34 [970]P36(f27(f28(f96(x9701,a2),x9702),x9703))+~P36(f27(f28(f96(x9701,a2),f27(f27(f6(x9701,f96(x9701,a2),a2),f34(x9701)),x9702)),f27(f27(f6(x9701,f96(x9701,a2),a2),f34(x9701)),x9703)))
% 1.10/1.34 [750]P36(f27(f28(a93,x7501),x7502))+~P36(f27(f28(a93,f27(f27(f19(a93),x7503),x7501)),x7502))
% 1.10/1.34 [751]P36(f27(f28(a93,x7511),x7512))+~P36(f27(f28(a93,f27(f27(f19(a93),x7511),x7513)),x7512))
% 1.10/1.34 [765]P36(f27(f27(f29(a93),x7651),x7652))+~P36(f27(f27(f29(a93),f27(f27(f19(a93),x7651),x7653)),x7652))
% 1.10/1.34 [808]~P18(x8081,x8083)+P36(f27(f27(f34(f98(x8081,x8081)),f27(f27(f32(x8081,x8081),x8082),x8082)),x8083))
% 1.10/1.34 [698]~P13(x6982,x6984)+P13(x6981,f36(x6982,x6981,x6983,x6984))
% 1.10/1.34 [772]P13(x7721,x7722)+~P13(f97(x7723,x7721),f37(x7723,x7721,x7724,x7722))
% 1.10/1.34 [773]P13(x7731,x7732)+~P13(f97(x7731,x7733),f37(x7731,x7733,x7732,x7734))
% 1.10/1.34 [801]P14(x8011,x8012,x8013,x8014)+~E(f60(x8014,x8013,x8012,x8011),f63(x8014,x8013,x8012,x8011))
% 1.10/1.34 [567]~E(x5672,x5674)+P36(f27(f35(x5671,x5672,x5673),x5674))
% 1.10/1.34 [595]~P36(f27(x5953,x5954))+P36(f27(f35(x5951,x5952,x5953),x5954))
% 1.10/1.34 [617]~E(x6172,x6173)+P36(f27(f27(f34(x6171),x6172),f35(x6171,x6173,x6174)))
% 1.10/1.34 [709]P13(x7092,x7094)+E(f14(f97(x7091,x7092),f37(x7091,x7092,x7093,x7094)),f3(a93))
% 1.10/1.34 [710]P13(x7101,x7103)+E(f14(f97(x7101,x7102),f37(x7101,x7102,x7103,x7104)),f3(a93))
% 1.10/1.34 [786]~P14(x7862,x7861,x7863,x7864)+E(f14(x7861,f36(x7862,x7861,x7863,x7864)),f14(x7862,x7864))
% 1.10/1.34 [817]~P14(x8171,x8172,x8173,f30(f96(x8171,a2)))+E(f27(f22(x8171,x8172,f30(f96(x8171,a2)),x8173),f27(x8173,x8174)),x8174)
% 1.10/1.34 [832]P14(x8324,x8323,x8321,x8322)+E(f27(x8321,f60(x8322,x8321,x8323,x8324)),f27(x8321,f63(x8322,x8321,x8323,x8324)))
% 1.10/1.34 [846]P36(f27(f27(f34(f98(x8461,x8461)),f27(f27(f32(x8461,x8461),x8462),x8463)),f40(x8461,x8464)))+~P36(f27(f27(f29(a93),f27(x8464,x8462)),f27(x8464,x8463)))
% 1.10/1.34 [857]~P14(x8572,x8571,x8573,f30(f96(x8572,a2)))+E(f36(x8571,x8572,f22(x8572,x8571,f30(f96(x8572,a2)),x8573),f36(x8572,x8571,x8573,x8574)),x8574)
% 1.10/1.34 [864]~P36(f27(f27(f34(f98(x8644,x8644)),f27(f27(f32(x8644,x8644),x8642),x8643)),f40(x8644,x8641)))+P36(f27(f27(f29(a93),f27(x8641,x8642)),f27(x8641,x8643)))
% 1.10/1.34 [941]~P13(x9412,x9414)+P36(f27(f28(a93,f14(x9411,f36(x9412,x9411,x9413,x9414))),f14(x9412,x9414)))
% 1.10/1.34 [968]~P14(x9681,x9682,x9683,x9684)+~P36(f27(f27(f29(a93),f14(x9682,f36(x9681,x9682,x9683,x9684))),f14(x9681,x9684)))
% 1.10/1.34 [688]P36(f27(f27(f34(x6881),x6882),f35(x6881,x6883,x6884)))+~P36(f27(f27(f34(x6881),x6882),x6884))
% 1.10/1.34 [727]P36(f27(f28(f96(x7271,a2),x7272),f35(x7271,x7273,x7274)))+~P36(f27(f28(f96(x7271,a2),x7272),x7274))
% 1.10/1.34 [806]P36(f27(f27(f34(x8061),x8062),x8063))+~P36(f27(f28(f96(x8061,a2),f35(x8061,x8062,x8064)),x8063))
% 1.10/1.34 [809]P36(f27(f28(f96(x8091,a2),f35(x8091,x8092,x8093)),f35(x8091,x8092,x8094)))+~P36(f27(f28(f96(x8091,a2),x8093),x8094))
% 1.10/1.34 [818]~P36(f27(f28(f96(x8181,a2),f35(x8181,x8184,x8182)),x8183))+P36(f27(f28(f96(x8181,a2),x8182),x8183))
% 1.10/1.34 [848]~E(x8481,x8482)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x8483),x8481)),f27(f27(a12,x8484),x8482)))
% 1.10/1.34 [849]~E(x8491,x8492)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x8491),x8493)),f27(f27(a10,x8494),x8492)))
% 1.10/1.34 [866]~P14(x8661,x8663,x8664,f30(f96(x8661,a2)))+P14(x8661,f96(x8662,x8663),f27(f9(x8663,f96(x8662,x8663),x8661,f15(x8663,x8662)),x8664),f30(f96(x8661,a2)))
% 1.10/1.34 [874]P14(x8741,x8742,x8743,x8744)+P36(f27(f27(f34(x8741),f60(x8744,x8743,x8742,x8741)),x8744))
% 1.10/1.34 [875]P14(x8751,x8752,x8753,x8754)+P36(f27(f27(f34(x8751),f63(x8754,x8753,x8752,x8751)),x8754))
% 1.10/1.34 [608]~P31(x6081)+E(f27(f27(f19(x6081),x6082),f27(f27(f19(x6081),x6083),x6084)),f27(f27(f19(x6081),x6083),f27(f27(f19(x6081),x6082),x6084)))
% 1.10/1.34 [666]~P11(x6661)+E(f27(f27(f19(x6661),f27(f27(f19(x6661),x6662),x6663)),x6664),f27(f27(f19(x6661),x6662),f27(f27(f19(x6661),x6663),x6664)))
% 1.10/1.34 [667]~P31(x6671)+E(f27(f27(f19(x6671),f27(f27(f19(x6671),x6672),x6673)),x6674),f27(f27(f19(x6671),x6672),f27(f27(f19(x6671),x6673),x6674)))
% 1.10/1.34 [696]~P31(x6961)+E(f27(f27(f19(x6961),f27(f27(f19(x6961),x6962),x6963)),x6964),f27(f27(f19(x6961),f27(f27(f19(x6961),x6962),x6964)),x6963))
% 1.10/1.34 [854]~E(f36(x8542,x8543,x8541,f30(f96(x8542,a2))),f30(f96(x8543,a2)))+E(f27(x8541,f27(f22(x8542,x8543,f30(f96(x8542,a2)),x8541),x8544)),x8544)
% 1.10/1.34 [881]~E(f36(x8811,x8812,x8813,f30(f96(x8811,a2))),f30(f96(x8812,a2)))+E(f36(x8811,x8812,x8813,f36(x8812,x8811,f22(x8811,x8812,f30(f96(x8811,a2)),x8813),x8814)),x8814)
% 1.10/1.34 [1011]P19(x10111,f27(f27(f6(x10111,f96(f98(x10111,x10111),a2),f96(x10111,a2)),f27(f9(f96(x10111,f96(f96(f98(x10111,x10111),a2),a2)),f96(f96(f98(x10111,x10111),a2),f96(x10111,a2)),x10111,f6(x10111,f96(f98(x10111,x10111),a2),a2)),f27(f9(f96(x10111,f98(x10111,x10111)),f96(x10111,f96(f96(f98(x10111,x10111),a2),a2)),x10111,f9(f98(x10111,x10111),f96(f96(f98(x10111,x10111),a2),a2),x10111,f34(f98(x10111,x10111)))),f32(x10111,x10111)))),x10112),x10113,x10114)+~P36(f27(f27(f34(f98(f96(x10111,a2),f96(x10111,a2))),f27(f27(f32(f96(x10111,a2),f96(x10111,a2)),x10113),x10114)),f43(x10111,x10112)))
% 1.10/1.34 [1017]E(x10171,x10172)+~E(f27(f27(f6(x10173,f96(f98(x10173,x10174),a2),f96(x10174,a2)),f27(f9(f96(x10174,f96(f96(f98(x10173,x10174),a2),a2)),f96(f96(f98(x10173,x10174),a2),f96(x10174,a2)),x10173,f6(x10174,f96(f98(x10173,x10174),a2),a2)),f27(f9(f96(x10174,f98(x10173,x10174)),f96(x10174,f96(f96(f98(x10173,x10174),a2),a2)),x10173,f9(f98(x10173,x10174),f96(f96(f98(x10173,x10174),a2),a2),x10174,f34(f98(x10173,x10174)))),f32(x10173,x10174)))),x10171),f27(f27(f6(x10173,f96(f98(x10173,x10174),a2),f96(x10174,a2)),f27(f9(f96(x10174,f96(f96(f98(x10173,x10174),a2),a2)),f96(f96(f98(x10173,x10174),a2),f96(x10174,a2)),x10173,f6(x10174,f96(f98(x10173,x10174),a2),a2)),f27(f9(f96(x10174,f98(x10173,x10174)),f96(x10174,f96(f96(f98(x10173,x10174),a2),a2)),x10173,f9(f98(x10173,x10174),f96(f96(f98(x10173,x10174),a2),a2),x10174,f34(f98(x10173,x10174)))),f32(x10173,x10174)))),x10172))
% 1.10/1.34 [1018]~P19(x10181,f27(f27(f6(x10181,f96(f98(x10181,x10181),a2),f96(x10181,a2)),f27(f9(f96(x10181,f96(f96(f98(x10181,x10181),a2),a2)),f96(f96(f98(x10181,x10181),a2),f96(x10181,a2)),x10181,f6(x10181,f96(f98(x10181,x10181),a2),a2)),f27(f9(f96(x10181,f98(x10181,x10181)),f96(x10181,f96(f96(f98(x10181,x10181),a2),a2)),x10181,f9(f98(x10181,x10181),f96(f96(f98(x10181,x10181),a2),a2),x10181,f34(f98(x10181,x10181)))),f32(x10181,x10181)))),x10184),x10182,x10183)+P36(f27(f27(f34(f98(f96(x10181,a2),f96(x10181,a2))),f27(f27(f32(f96(x10181,a2),f96(x10181,a2)),x10182),x10183)),f43(x10181,x10184)))
% 1.10/1.34 [1024]~P36(f27(f28(f96(f98(x10241,x10242),a2),x10243),x10244))+P36(f27(f28(f96(x10241,f96(x10242,a2)),f27(f27(f6(x10241,f96(f98(x10241,x10242),a2),f96(x10242,a2)),f27(f9(f96(x10242,f96(f96(f98(x10241,x10242),a2),a2)),f96(f96(f98(x10241,x10242),a2),f96(x10242,a2)),x10241,f6(x10242,f96(f98(x10241,x10242),a2),a2)),f27(f9(f96(x10242,f98(x10241,x10242)),f96(x10242,f96(f96(f98(x10241,x10242),a2),a2)),x10241,f9(f98(x10241,x10242),f96(f96(f98(x10241,x10242),a2),a2),x10242,f34(f98(x10241,x10242)))),f32(x10241,x10242)))),x10243)),f27(f27(f6(x10241,f96(f98(x10241,x10242),a2),f96(x10242,a2)),f27(f9(f96(x10242,f96(f96(f98(x10241,x10242),a2),a2)),f96(f96(f98(x10241,x10242),a2),f96(x10242,a2)),x10241,f6(x10242,f96(f98(x10241,x10242),a2),a2)),f27(f9(f96(x10242,f98(x10241,x10242)),f96(x10242,f96(f96(f98(x10241,x10242),a2),a2)),x10241,f9(f98(x10241,x10242),f96(f96(f98(x10241,x10242),a2),a2),x10242,f34(f98(x10241,x10242)))),f32(x10241,x10242)))),x10244)))
% 1.10/1.34 [1025]P36(f27(f28(f96(f98(x10251,x10252),a2),x10253),x10254))+~P36(f27(f28(f96(x10251,f96(x10252,a2)),f27(f27(f6(x10251,f96(f98(x10251,x10252),a2),f96(x10252,a2)),f27(f9(f96(x10252,f96(f96(f98(x10251,x10252),a2),a2)),f96(f96(f98(x10251,x10252),a2),f96(x10252,a2)),x10251,f6(x10252,f96(f98(x10251,x10252),a2),a2)),f27(f9(f96(x10252,f98(x10251,x10252)),f96(x10252,f96(f96(f98(x10251,x10252),a2),a2)),x10251,f9(f98(x10251,x10252),f96(f96(f98(x10251,x10252),a2),a2),x10252,f34(f98(x10251,x10252)))),f32(x10251,x10252)))),x10253)),f27(f27(f6(x10251,f96(f98(x10251,x10252),a2),f96(x10252,a2)),f27(f9(f96(x10252,f96(f96(f98(x10251,x10252),a2),a2)),f96(f96(f98(x10251,x10252),a2),f96(x10252,a2)),x10251,f6(x10252,f96(f98(x10251,x10252),a2),a2)),f27(f9(f96(x10252,f98(x10251,x10252)),f96(x10252,f96(f96(f98(x10251,x10252),a2),a2)),x10251,f9(f98(x10251,x10252),f96(f96(f98(x10251,x10252),a2),a2),x10252,f34(f98(x10251,x10252)))),f32(x10251,x10252)))),x10254)))
% 1.10/1.34 [852]P36(f27(f27(f34(f98(x8521,x8521)),f27(f27(f32(x8521,x8521),x8522),x8523)),f44(x8521,x8524,x8525)))+~P36(f27(f27(f29(a93),f27(x8524,x8522)),f27(x8524,x8523)))
% 1.10/1.34 [871]E(f27(x8711,f74(x8712,x8711,x8713,x8714)),x8714)+~P36(f27(f27(f34(x8715),x8714),f36(x8713,x8715,x8711,x8712)))
% 1.10/1.34 [887]P14(x8871,x8872,f22(x8872,x8871,x8873,x8874),x8875)+~P36(f27(f28(f96(x8871,a2),x8875),f36(x8872,x8871,x8874,x8873)))
% 1.10/1.34 [944]E(f36(x9441,x9442,x9443,f79(x9444,x9443,x9441,x9445,x9442)),x9445)+~P36(f27(f28(f96(x9442,a2),x9445),f36(x9441,x9442,x9443,x9444)))
% 1.10/1.34 [795]E(f35(x7951,f27(x7952,x7953),f36(x7954,x7951,x7952,x7955)),f36(x7954,x7951,x7952,x7955))+~P36(f27(f27(f34(x7954),x7953),x7955))
% 1.10/1.34 [840]P36(f27(f27(f34(x8401),f27(x8402,x8403)),f36(x8404,x8401,x8402,x8405)))+~P36(f27(f27(f34(x8404),x8403),x8405))
% 1.10/1.34 [892]E(f27(x8921,f27(f22(x8922,x8923,x8924,x8921),x8925)),x8925)+~P36(f27(f27(f34(x8923),x8925),f36(x8922,x8923,x8921,x8924)))
% 1.10/1.34 [907]P36(f27(f28(f96(x9071,a2),f36(x9072,x9071,x9073,x9074)),f36(x9072,x9071,x9073,x9075)))+~P36(f27(f28(f96(x9072,a2),x9074),x9075))
% 1.10/1.34 [919]~P13(x9193,f36(x9192,x9193,x9195,f30(f96(x9192,a2))))+P13(x9191,f36(x9192,x9191,f27(f9(x9193,x9191,x9192,x9194),x9195),f30(f96(x9192,a2))))
% 1.10/1.34 [926]P36(f27(f28(f96(f96(x9261,x9262),a2),f17(x9261,x9262,x9263,x9264)),f17(x9261,x9262,x9265,x9264)))+~P36(f27(f28(f96(x9261,a2),x9265),x9263))
% 1.10/1.34 [935]~P36(f27(f27(f34(x9355),x9354),f36(x9351,x9355,x9353,x9352)))+P36(f27(f27(f34(x9351),f74(x9352,x9353,x9351,x9354)),x9352))
% 1.10/1.34 [983]P36(f27(f27(f34(f96(x9831,x9834)),x9833),f17(x9831,x9834,x9835,x9832)))+P36(f27(f27(f34(x9831),f68(x9832,x9833,x9834,x9835,x9831)),x9835))
% 1.10/1.34 [984]~P36(f27(f28(f96(x9845,a2),x9844),f36(x9841,x9845,x9843,x9842)))+P36(f27(f28(f96(x9841,a2),f79(x9842,x9843,x9841,x9844,x9845)),x9842))
% 1.10/1.34 [989]P36(f27(f28(f96(f96(x9891,x9894),a2),f17(x9891,x9894,x9895,x9893)),f17(x9891,x9894,x9895,x9892)))+P36(f27(f27(f34(x9891),f70(x9892,x9893,x9894,x9895,x9891)),x9895))
% 1.10/1.34 [1009]P36(f27(f27(f34(f96(x10091,x10092)),x10093),f17(x10091,x10092,x10094,x10095)))+~P36(f27(f27(f34(x10092),f27(x10093,f68(x10095,x10093,x10092,x10094,x10091))),f27(x10095,f68(x10095,x10093,x10092,x10094,x10091))))
% 1.10/1.34 [1010]P36(f27(f28(f96(f96(x10101,x10102),a2),f17(x10101,x10102,x10103,x10104)),f17(x10101,x10102,x10103,x10105)))+~P36(f27(f28(f96(x10102,a2),f27(x10104,f70(x10105,x10104,x10102,x10103,x10101))),f27(x10105,f70(x10105,x10104,x10102,x10103,x10101))))
% 1.10/1.34 [742]~P31(x7421)+E(f27(f27(f19(x7421),f27(f27(f19(x7421),x7422),x7423)),f27(f27(f19(x7421),x7424),x7425)),f27(f27(f19(x7421),f27(f27(f19(x7421),x7422),x7424)),f27(f27(f19(x7421),x7423),x7425)))
% 1.10/1.34 [839]~E(x8392,f27(x8394,x8395))+P36(f27(f27(f34(x8391),x8392),f36(x8393,x8391,x8394,f30(f96(x8393,a2)))))
% 1.10/1.34 [962]~P36(f27(f27(f34(x9622),x9625),f36(x9621,x9622,x9624,x9623)))+P36(f27(f27(f34(x9621),f27(f22(x9621,x9622,x9623,x9624),x9625)),x9623))
% 1.10/1.34 [895]P15(x8951,x8952,x8953,x8954,x8955)+~P36(f27(f27(f34(f98(x8951,x8952)),f27(f27(f32(x8951,x8952),x8954),x8955)),x8953))
% 1.10/1.34 [900]~P15(x9001,x9002,x9005,x9003,x9004)+P36(f27(f27(f34(f98(x9001,x9002)),f27(f27(f32(x9001,x9002),x9003),x9004)),x9005))
% 1.10/1.34 [958]P36(f27(f28(f96(x9581,a2),f36(x9582,x9581,x9583,x9584)),x9585))+~P36(f27(f27(f34(f96(x9582,x9581)),x9583),f17(x9582,x9581,x9584,f27(f15(f96(x9581,a2),x9582),x9585))))
% 1.10/1.34 [974]~P16(x9743,x9744,x9741,x9745,x9746,x9747)+E(f27(f27(x9741,x9742),x9742),x9742)
% 1.10/1.34 [980]P36(f27(f27(f34(f98(f98(x9801,x9802),f98(x9801,x9802))),f27(f27(f32(f98(x9801,x9802),f98(x9801,x9802)),f27(f27(f32(x9801,x9802),x9803),x9804)),f27(f27(f32(x9801,x9802),x9805),x9806))),f42(x9801,x9802,x9807,x9808)))+~P36(f27(f27(f34(f98(x9801,x9801)),f27(f27(f32(x9801,x9801),x9803),x9805)),x9807))
% 1.10/1.34 [873]P1(x8731)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),f53(x8731)),f54(x8731))),f27(x8731,f52(x8731))))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),f53(x8731)),f54(x8731))),f27(x8731,f51(x8731))))
% 1.10/1.34 [914]P1(x9141)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),f53(x9141)),f54(x9141))),f27(x9141,f52(x9141))))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),f53(x9141)),f54(x9141))),f27(x9141,f51(x9141))))
% 1.10/1.34 [898]~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(a104,x8981)))+~P36(f27(f27(f29(a93),f27(a99,x8981)),a108))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(f27(a10,f27(a104,x8981)),a107)))
% 1.10/1.34 [904]P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(a104,x9041)))+~P36(f27(f27(f29(a93),f27(a99,x9041)),a108))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(f27(a10,f27(a104,x9041)),a107)))
% 1.10/1.34 [419]~P12(x4192)+~P12(x4191)+P12(f98(x4191,x4192))
% 1.10/1.34 [420]~P12(x4202)+~P12(x4201)+P12(f96(x4201,x4202))
% 1.10/1.34 [421]~P12(x4212)+~P12(x4211)+P12(f97(x4211,x4212))
% 1.10/1.34 [555]E(x5551,x5552)+~P36(f27(f28(a93,x5552),x5551))+~P36(f27(f28(a93,x5551),x5552))
% 1.10/1.34 [580]E(x5801,f3(a93))+E(f27(a21,f71(x5802,x5801)),x5801)+~P36(f27(f27(f29(a93),x5801),f27(a21,x5802)))
% 1.10/1.34 [588]E(x5881,f27(a21,x5882))+P36(f27(f28(a93,x5881),x5882))+~P36(f27(f28(a93,x5881),f27(a21,x5882)))
% 1.10/1.34 [625]E(x6251,x6252)+~P36(f27(f28(a93,x6252),x6251))+~P36(f27(f27(f29(a93),x6251),f27(a21,x6252)))
% 1.10/1.34 [726]~P23(x7261)+~P36(f27(f28(x7261,x7262),f3(x7261)))+P36(f27(f28(x7261,f27(f27(f19(x7261),x7262),x7262)),f3(x7261)))
% 1.10/1.34 [740]~P32(x7401)+~P36(f27(f27(f29(x7401),x7402),f3(x7401)))+P36(f27(f27(f29(x7401),f27(f27(f19(x7401),x7402),x7402)),f3(x7401)))
% 1.10/1.34 [741]~P23(x7411)+~P36(f27(f27(f29(x7411),x7412),f3(x7411)))+P36(f27(f27(f29(x7411),f27(f27(f19(x7411),x7412),x7412)),f3(x7411)))
% 1.10/1.34 [778]~P23(x7781)+~P36(f27(f28(x7781,f27(f27(f19(x7781),x7782),x7782)),f3(x7781)))+P36(f27(f28(x7781,x7782),f3(x7781)))
% 1.10/1.34 [791]~P32(x7911)+~P36(f27(f27(f29(x7911),f27(f27(f19(x7911),x7912),x7912)),f3(x7911)))+P36(f27(f27(f29(x7911),x7912),f3(x7911)))
% 1.10/1.34 [792]~P23(x7921)+~P36(f27(f27(f29(x7921),f27(f27(f19(x7921),x7922),x7922)),f3(x7921)))+P36(f27(f27(f29(x7921),x7922),f3(x7921)))
% 1.10/1.34 [422]~E(x4222,f3(a93))+~E(x4221,f3(a93))+E(f27(f27(f19(a93),x4221),x4222),f3(a93))
% 1.10/1.34 [428]~P23(x4281)+~E(x4282,f3(x4281))+E(f27(f27(f19(x4281),x4282),x4282),f3(x4281))
% 1.10/1.34 [449]~E(x4492,f3(a93))+~E(x4491,f27(a21,f3(a93)))+E(f27(f27(f19(a93),x4491),x4492),f27(a21,f3(a93)))
% 1.10/1.34 [450]~E(x4501,f3(a93))+~E(x4502,f27(a21,f3(a93)))+E(f27(f27(f19(a93),x4501),x4502),f27(a21,f3(a93)))
% 1.10/1.34 [453]~P23(x4532)+E(x4531,f3(x4532))+~E(f27(f27(f19(x4532),x4531),x4531),f3(x4532))
% 1.10/1.34 [456]E(x4561,f3(a93))+E(x4562,f3(a93))+~E(f27(f27(f19(a93),x4562),x4561),f27(a21,f3(a93)))
% 1.10/1.34 [462]E(x4621,f3(a93))+E(x4621,f27(a21,f3(a93)))+~E(f27(f27(f19(a93),x4622),x4621),f27(a21,f3(a93)))
% 1.10/1.34 [463]E(x4631,f3(a93))+E(x4631,f27(a21,f3(a93)))+~E(f27(f27(f19(a93),x4631),x4632),f27(a21,f3(a93)))
% 1.10/1.34 [469]E(x4691,f27(a21,f3(a93)))+E(x4692,f27(a21,f3(a93)))+~E(f27(f27(f19(a93),x4691),x4692),f27(a21,f3(a93)))
% 1.10/1.34 [518]E(x5181,x5182)+P36(f27(f27(f29(a93),x5182),x5181))+P36(f27(f27(f29(a93),x5181),x5182))
% 1.10/1.34 [534]E(x5341,x5342)+~P36(f27(f28(a93,x5341),x5342))+P36(f27(f27(f29(a93),x5341),x5342))
% 1.10/1.34 [572]~P13(a93,x5722)+P36(f27(f28(a93,x5721),f84(x5722)))+~P36(f27(f27(f34(a93),x5721),x5722))
% 1.10/1.34 [574]E(x5741,f30(f96(x5742,a2)))+~P13(x5742,f30(f96(x5742,a2)))+~E(f14(x5742,x5741),f14(x5742,f30(f96(x5742,a2))))
% 1.10/1.34 [586]~P13(a93,x5862)+P36(f27(f27(f29(a93),x5861),f81(x5862)))+~P36(f27(f27(f34(a93),x5861),x5862))
% 1.10/1.34 [589]~P36(f27(x5891,x5892))+P36(f27(x5891,f3(a93)))+P36(f27(f27(f29(a93),f72(x5892,x5891)),x5892))
% 1.10/1.34 [615]E(x6151,x6152)+~P36(f27(f27(f29(a93),x6151),f27(a21,x6152)))+P36(f27(f27(f29(a93),x6151),x6152))
% 1.10/1.34 [633]E(f27(a21,x6331),x6332)+~P36(f27(f27(f29(a93),x6331),x6332))+P36(f27(f27(f29(a93),f27(a21,x6331)),x6332))
% 1.10/1.34 [655]~P13(x6552,f30(f96(x6552,a2)))+~P13(x6551,f30(f96(x6551,a2)))+P13(f98(x6551,x6552),f30(f96(f98(x6551,x6552),a2)))
% 1.10/1.34 [656]~P13(x6562,f30(f96(x6562,a2)))+~P13(x6561,f30(f96(x6561,a2)))+P13(f97(x6561,x6562),f30(f96(f97(x6561,x6562),a2)))
% 1.10/1.34 [668]E(x6681,f3(a93))+~P36(f27(f27(f29(a93),x6681),f27(a21,x6682)))+P36(f27(f27(f29(a93),f71(x6682,x6681)),x6682))
% 1.10/1.34 [679]P13(x6792,f30(f96(x6792,a2)))+E(f14(x6791,f30(f96(x6791,a2))),f27(a21,f3(a93)))+~P13(f96(x6792,x6791),f30(f96(f96(x6792,x6791),a2)))
% 1.10/1.34 [689]~P36(f27(x6891,x6892))+P36(f27(x6891,f3(a93)))+P36(f27(x6891,f27(f27(f19(a93),f72(x6892,x6891)),f4(a93))))
% 1.10/1.34 [783]~P14(x7831,x7831,x7832,f30(f96(x7831,a2)))+~P13(x7831,f30(f96(x7831,a2)))+E(f36(x7831,x7831,x7832,f30(f96(x7831,a2))),f30(f96(x7831,a2)))
% 1.10/1.34 [788]P14(x7881,x7881,x7882,f30(f96(x7881,a2)))+~P13(x7881,f30(f96(x7881,a2)))+~E(f36(x7881,x7881,x7882,f30(f96(x7881,a2))),f30(f96(x7881,a2)))
% 1.10/1.34 [896]P1(x8961)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),f53(x8961)),f54(x8961))),f27(f52(x8961),x8962)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),f53(x8961)),f54(x8961))),f27(f51(x8961),x8962)))
% 1.10/1.34 [897]P1(x8971)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),f53(x8971)),f54(x8971))),f27(f51(x8971),x8972)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),f53(x8971)),f54(x8971))),f27(f52(x8971),x8972)))
% 1.10/1.34 [685]~P23(x6851)+~P36(f27(f28(x6851,f3(x6851)),x6852))+P36(f27(f28(x6851,f3(x6851)),f27(f27(f19(x6851),x6852),x6852)))
% 1.10/1.34 [708]~P23(x7081)+~P36(f27(f27(f29(x7081),f3(x7081)),x7082))+P36(f27(f27(f29(x7081),f3(x7081)),f27(f27(f19(x7081),x7082),x7082)))
% 1.10/1.34 [717]~P23(x7171)+P36(f27(f28(x7171,f3(x7171)),x7172))+~P36(f27(f28(x7171,f3(x7171)),f27(f27(f19(x7171),x7172),x7172)))
% 1.10/1.34 [729]P36(f27(f27(f29(a93),f3(a93)),x7292))+P36(f27(f27(f29(a93),f3(a93)),x7291))+~P36(f27(f27(f29(a93),f3(a93)),f27(f27(f19(a93),x7292),x7291)))
% 1.10/1.34 [730]~P23(x7301)+P36(f27(f27(f29(x7301),f3(x7301)),x7302))+~P36(f27(f27(f29(x7301),f3(x7301)),f27(f27(f19(x7301),x7302),x7302)))
% 1.10/1.34 [731]~P27(x7311)+~P36(f27(f27(f34(x7311),x7312),f24(x7311)))+~E(f27(f27(f19(x7311),f27(f27(f19(x7311),f4(x7311)),x7312)),x7312),f3(x7311))
% 1.10/1.34 [997]P3(x9971,x9972)+~E(f62(x9972,x9971),f57(x9972,x9971))+~P36(f27(f27(f34(f96(f96(a91,f96(f98(a92,a92),a2)),f96(f98(a92,a92),a2))),x9971),f17(f96(a91,f96(f98(a92,a92),a2)),f96(f98(a92,a92),a2),a8,f27(f15(f96(f96(f98(a92,a92),a2),a2),f96(a91,f96(f98(a92,a92),a2))),a7))))
% 1.10/1.34 [998]P3(x9981,x9982)+P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),f58(x9982,x9981)),a8))+~P36(f27(f27(f34(f96(f96(a91,f96(f98(a92,a92),a2)),f96(f98(a92,a92),a2))),x9981),f17(f96(a91,f96(f98(a92,a92),a2)),f96(f98(a92,a92),a2),a8,f27(f15(f96(f96(f98(a92,a92),a2),a2),f96(a91,f96(f98(a92,a92),a2))),a7))))
% 1.10/1.34 [999]P3(x9991,x9992)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),f57(x9992,x9991)),f62(x9992,x9991))),f27(f58(x9992,x9991),x9992)))+~P36(f27(f27(f34(f96(f96(a91,f96(f98(a92,a92),a2)),f96(f98(a92,a92),a2))),x9991),f17(f96(a91,f96(f98(a92,a92),a2)),f96(f98(a92,a92),a2),a8,f27(f15(f96(f96(f98(a92,a92),a2),a2),f96(a91,f96(f98(a92,a92),a2))),a7))))
% 1.10/1.34 [1000]P3(x10001,x10002)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),f57(x10002,x10001)),f62(x10002,x10001))),f27(x10001,f58(x10002,x10001))))+~P36(f27(f27(f34(f96(f96(a91,f96(f98(a92,a92),a2)),f96(f98(a92,a92),a2))),x10001),f17(f96(a91,f96(f98(a92,a92),a2)),f96(f98(a92,a92),a2),a8,f27(f15(f96(f96(f98(a92,a92),a2),a2),f96(a91,f96(f98(a92,a92),a2))),a7))))
% 1.10/1.34 [444]~E(x4442,x4443)+~P5(x4441)+P36(f27(f28(x4441,x4442),x4443))
% 1.10/1.34 [446]~E(x4462,x4463)+~P28(x4461)+P36(f27(f28(x4461,x4462),x4463))
% 1.10/1.34 [494]~P6(x4941)+P36(f27(f28(x4941,x4943),x4942))+P36(f27(f28(x4941,x4942),x4943))
% 1.10/1.34 [607]~P36(f27(f28(a93,x6071),x6073))+P36(f27(f28(a93,x6071),x6072))+~P36(f27(f28(a93,x6073),x6072))
% 1.10/1.34 [869]~P13(x8691,x8693)+P14(x8691,x8691,x8692,x8693)+~P36(f27(f28(f96(x8691,a2),x8693),f36(x8691,x8691,x8692,x8693)))
% 1.10/1.34 [426]~P35(x4261)+~E(x4263,f3(x4261))+E(f27(f27(f19(x4261),x4262),x4263),x4262)
% 1.10/1.34 [451]~P35(x4512)+E(x4511,f3(x4512))+~E(f27(f27(f19(x4512),x4513),x4511),x4513)
% 1.10/1.34 [514]~E(x5141,x5142)+~P6(x5143)+~P36(f27(f27(f29(x5143),x5141),x5142))
% 1.10/1.34 [515]~E(x5151,x5152)+~P28(x5153)+~P36(f27(f27(f29(x5153),x5151),x5152))
% 1.10/1.34 [525]~P6(x5251)+P36(f27(f28(x5251,x5252),x5253))+P36(f27(f27(f29(x5251),x5253),x5252))
% 1.10/1.34 [569]~P5(x5691)+P36(f27(f28(x5691,x5692),x5693))+~P36(f27(f27(f29(x5691),x5692),x5693))
% 1.10/1.34 [571]~P28(x5711)+P36(f27(f28(x5711,x5712),x5713))+~P36(f27(f27(f29(x5711),x5712),x5713))
% 1.10/1.34 [594]~P13(x5941,x5943)+E(f14(x5941,f35(x5941,x5942,x5943)),f27(a21,f14(x5941,x5943)))+P36(f27(f27(f34(x5941),x5942),x5943))
% 1.10/1.34 [599]~P5(x5991)+~P36(f27(f28(x5991,x5992),x5993))+~P36(f27(f27(f29(x5991),x5993),x5992))
% 1.10/1.34 [602]~P6(x6021)+~P36(f27(f28(x6021,x6022),x6023))+~P36(f27(f27(f29(x6021),x6023),x6022))
% 1.10/1.34 [605]P13(x6051,x6052)+~P13(x6051,x6053)+~P36(f27(f28(f96(x6051,a2),x6052),x6053))
% 1.10/1.34 [606]~E(x6061,f27(a21,x6063))+P36(f27(f27(f29(a93),x6061),f27(a21,x6062)))+~P36(f27(f27(f29(a93),x6063),x6062))
% 1.10/1.34 [619]~P13(x6191,x6193)+E(f14(x6191,f35(x6191,x6192,x6193)),f14(x6191,x6193))+~P36(f27(f27(f34(x6191),x6192),x6193))
% 1.10/1.34 [621]~P13(x6211,x6213)+E(f14(x6211,f35(x6211,x6212,x6213)),f27(f27(f19(a93),f4(a93)),f14(x6211,x6213)))+P36(f27(f27(f34(x6211),x6212),x6213))
% 1.10/1.34 [630]~P5(x6301)+~P36(f27(f27(f29(x6301),x6303),x6302))+~P36(f27(f27(f29(x6301),x6302),x6303))
% 1.10/1.34 [631]~P6(x6311)+~P36(f27(f27(f29(x6311),x6313),x6312))+~P36(f27(f27(f29(x6311),x6312),x6313))
% 1.10/1.34 [632]~P28(x6321)+~P36(f27(f27(f29(x6321),x6323),x6322))+~P36(f27(f27(f29(x6321),x6322),x6323))
% 1.10/1.34 [684]~P36(f27(f27(f29(a93),x6841),x6843))+~P36(f27(f27(f29(a93),x6843),x6842))+P36(f27(f27(f29(a93),f27(a21,x6841)),x6842))
% 1.10/1.34 [697]~P13(x6971,x6973)+P36(f27(f28(a93,f14(x6971,x6972)),f14(x6971,x6973)))+~P36(f27(f28(f96(x6971,a2),x6972),x6973))
% 1.10/1.34 [707]E(x7071,x7072)+~P36(f27(f28(f96(x7073,a2),x7071),x7072))+~P36(f27(f28(f96(x7073,a2),x7072),x7071))
% 1.10/1.34 [712]E(x7121,x7122)+~P36(f27(f28(f96(x7123,a2),x7121),x7122))+P36(f27(f27(f29(f96(x7123,a2)),x7121),x7122))
% 1.10/1.34 [743]~P13(x7431,x7433)+P36(f27(f27(f29(a93),f14(x7431,x7432)),f14(x7431,x7433)))+~P36(f27(f27(f29(f96(x7431,a2)),x7432),x7433))
% 1.10/1.34 [928]~P13(x9281,x9283)+P36(f27(f27(f34(f98(f96(x9281,a2),f96(x9281,a2))),f27(f27(f32(f96(x9281,a2),f96(x9281,a2)),x9282),x9283)),f41(x9281)))+~P36(f27(f27(f29(f96(x9281,a2)),x9282),x9283))
% 1.10/1.34 [865]E(x8651,x8652)+P36(f27(f27(f34(f96(f98(a92,a92),a2)),f13(x8653,x8651,x8652)),a7))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x8653),a7))
% 1.10/1.34 [872]E(x8721,x8722)+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x8723),a7))+P36(f27(f27(f34(f96(f98(a92,a92),a2)),f27(f27(f27(a11,x8723),x8721),x8722)),a7))
% 1.10/1.34 [930]~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9303),x9302)),x9301))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9302),x9303)),x9301))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9301),a7))
% 1.10/1.34 [868]~P3(x8681,x8683)+E(f27(x8681,x8682),f27(x8682,x8683))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x8682),a8))
% 1.10/1.34 [714]~P13(x7142,x7144)+~P13(x7141,x7143)+P13(f97(x7141,x7142),f37(x7141,x7142,x7143,x7144))
% 1.10/1.34 [826]P13(x8261,x8262)+~P14(x8261,x8263,x8264,x8262)+~P13(x8263,f36(x8261,x8263,x8264,x8262))
% 1.10/1.34 [664]E(x6641,x6642)+P36(f27(x6643,x6642))+~P36(f27(f35(x6644,x6641,x6643),x6642))
% 1.10/1.34 [736]~P13(x7362,x7364)+~P13(x7361,x7363)+E(f14(f97(x7361,x7362),f37(x7361,x7362,x7363,x7364)),f27(f27(f19(a93),f14(x7361,x7363)),f14(x7362,x7364)))
% 1.10/1.34 [811]~P13(x8111,x8114)+P14(x8111,x8112,x8113,x8114)+~E(f14(x8112,f36(x8111,x8112,x8113,x8114)),f14(x8111,x8114))
% 1.10/1.34 [496]~P9(x4963)+E(x4961,x4962)+~E(f27(f27(f19(x4963),x4964),x4961),f27(f27(f19(x4963),x4964),x4962))
% 1.10/1.34 [497]~P10(x4973)+E(x4971,x4972)+~E(f27(f27(f19(x4973),x4974),x4971),f27(f27(f19(x4973),x4974),x4972))
% 1.10/1.34 [499]~P9(x4993)+E(x4991,x4992)+~E(f27(f27(f19(x4993),x4991),x4994),f27(f27(f19(x4993),x4992),x4994))
% 1.10/1.34 [637]P36(f27(x6371,x6372))+~P36(f27(x6373,x6372))+~P36(f27(f28(f96(x6374,a2),x6373),x6371))
% 1.10/1.34 [654]~E(f27(f27(f19(a93),x6543),x6542),f27(f27(f19(a93),x6541),x6544))+~P36(f27(f27(f29(a93),x6543),x6544))+P36(f27(f27(f29(a93),x6541),x6542))
% 1.10/1.34 [705]P36(f27(f27(f34(x7051),x7052),x7053))+~P36(f27(f27(f34(x7051),x7052),x7054))+~P36(f27(f28(f96(x7051,a2),x7054),x7053))
% 1.10/1.34 [719]E(x7191,x7192)+~P36(f27(f27(f34(x7193),x7191),f35(x7193,x7192,x7194)))+P36(f27(f27(f34(x7193),x7191),x7194))
% 1.10/1.34 [739]~P36(f27(f28(f96(x7391,a2),x7392),x7394))+~P36(f27(f28(f96(x7391,a2),x7394),x7393))+P36(f27(f28(f96(x7391,a2),x7392),x7393))
% 1.10/1.34 [777]~P36(f27(f28(f96(x7771,a2),x7773),f35(x7771,x7772,x7774)))+P36(f27(f27(f34(x7771),x7772),x7773))+P36(f27(f28(f96(x7771,a2),x7773),x7774))
% 1.10/1.34 [802]~P36(f27(f27(f34(x8021),x8022),x8024))+~P36(f27(f28(f96(x8021,a2),x8023),x8024))+P36(f27(f28(f96(x8021,a2),f35(x8021,x8022,x8023)),x8024))
% 1.10/1.34 [850]~E(x8501,x8502)+~E(x8501,x8503)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x8502),x8501)),f27(f27(a10,x8504),x8503)))
% 1.10/1.34 [851]~E(x8511,x8512)+~E(x8511,x8513)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x8511),x8512)),f27(f27(a12,x8514),x8513)))
% 1.10/1.34 [979]~P29(x9792)+~P36(f27(f28(x9792,f27(x9793,f61(x9794,x9793,x9791,x9792))),f27(x9794,f61(x9794,x9793,x9791,x9792))))+P36(f27(f28(f96(x9791,x9792),x9793),x9794))
% 1.10/1.34 [733]~P29(x7332)+P36(f27(f28(f96(x7331,x7332),x7333),x7334))+~P36(f27(f27(f29(f96(x7331,x7332)),x7333),x7334))
% 1.10/1.34 [744]P36(f27(f27(f34(x7441),x7442),x7443))+~P36(f27(f27(f34(x7441),x7442),x7444))+~P36(f27(f27(f29(f96(x7441,a2)),x7444),x7443))
% 1.10/1.34 [761]~P29(x7611)+~P36(f27(f28(f96(x7612,x7611),x7613),x7614))+~P36(f27(f27(f29(f96(x7612,x7611)),x7614),x7613))
% 1.10/1.34 [766]~P8(x7661)+~P36(f27(f28(x7661,x7663),x7664))+P36(f27(f28(x7661,f27(f27(f19(x7661),x7662),x7663)),f27(f27(f19(x7661),x7662),x7664)))
% 1.10/1.34 [767]~P24(x7671)+~P36(f27(f28(x7671,x7673),x7674))+P36(f27(f28(x7671,f27(f27(f19(x7671),x7672),x7673)),f27(f27(f19(x7671),x7672),x7674)))
% 1.10/1.34 [768]~P8(x7681)+~P36(f27(f28(x7681,x7682),x7684))+P36(f27(f28(x7681,f27(f27(f19(x7681),x7682),x7683)),f27(f27(f19(x7681),x7684),x7683)))
% 1.10/1.34 [769]~P24(x7691)+~P36(f27(f28(x7691,x7692),x7694))+P36(f27(f28(x7691,f27(f27(f19(x7691),x7692),x7693)),f27(f27(f19(x7691),x7694),x7693)))
% 1.10/1.34 [774]~P36(f27(f28(a93,x7742),x7744))+~P36(f27(f28(a93,x7741),x7743))+P36(f27(f28(a93,f27(f27(f19(a93),x7741),x7742)),f27(f27(f19(a93),x7743),x7744)))
% 1.10/1.34 [779]~P7(x7791)+~P36(f27(f27(f29(x7791),x7793),x7794))+P36(f27(f27(f29(x7791),f27(f27(f19(x7791),x7792),x7793)),f27(f27(f19(x7791),x7792),x7794)))
% 1.10/1.34 [780]~P8(x7801)+~P36(f27(f27(f29(x7801),x7803),x7804))+P36(f27(f27(f29(x7801),f27(f27(f19(x7801),x7802),x7803)),f27(f27(f19(x7801),x7802),x7804)))
% 1.10/1.34 [781]~P7(x7811)+~P36(f27(f27(f29(x7811),x7812),x7814))+P36(f27(f27(f29(x7811),f27(f27(f19(x7811),x7812),x7813)),f27(f27(f19(x7811),x7814),x7813)))
% 1.10/1.34 [782]~P8(x7821)+~P36(f27(f27(f29(x7821),x7822),x7824))+P36(f27(f27(f29(x7821),f27(f27(f19(x7821),x7822),x7823)),f27(f27(f19(x7821),x7824),x7823)))
% 1.10/1.34 [789]~P36(f27(f27(f29(a93),x7892),x7894))+~P36(f27(f27(f29(a93),x7891),x7893))+P36(f27(f27(f29(a93),f27(f27(f19(a93),x7891),x7892)),f27(f27(f19(a93),x7893),x7894)))
% 1.10/1.34 [797]~P36(f27(f28(f96(x7971,a2),x7974),x7973))+~P36(f27(f27(f29(f96(x7971,a2)),x7972),x7974))+P36(f27(f27(f29(f96(x7971,a2)),x7972),x7973))
% 1.10/1.34 [798]~P36(f27(f28(f96(x7981,a2),x7982),x7984))+~P36(f27(f27(f29(f96(x7981,a2)),x7984),x7983))+P36(f27(f27(f29(f96(x7981,a2)),x7982),x7983))
% 1.10/1.34 [822]~P8(x8221)+P36(f27(f28(x8221,x8222),x8223))+~P36(f27(f28(x8221,f27(f27(f19(x8221),x8224),x8222)),f27(f27(f19(x8221),x8224),x8223)))
% 1.10/1.34 [824]~P8(x8241)+P36(f27(f28(x8241,x8242),x8243))+~P36(f27(f28(x8241,f27(f27(f19(x8241),x8242),x8244)),f27(f27(f19(x8241),x8243),x8244)))
% 1.10/1.34 [825]~P36(f27(f27(f29(f96(x8251,a2)),x8252),x8254))+P36(f27(f27(f29(f96(x8251,a2)),x8252),x8253))+~P36(f27(f27(f29(f96(x8251,a2)),x8254),x8253))
% 1.10/1.34 [828]~P8(x8281)+P36(f27(f27(f29(x8281),x8282),x8283))+~P36(f27(f27(f29(x8281),f27(f27(f19(x8281),x8284),x8282)),f27(f27(f19(x8281),x8284),x8283)))
% 1.10/1.34 [830]~P8(x8301)+P36(f27(f27(f29(x8301),x8302),x8303))+~P36(f27(f27(f29(x8301),f27(f27(f19(x8301),x8302),x8304)),f27(f27(f19(x8301),x8303),x8304)))
% 1.10/1.34 [903]~P14(x9034,x9033,x9031,f30(f96(x9034,a2)))+E(f27(x9031,f76(x9032,x9031,x9033,x9034)),x9032)+~P36(f27(f27(f34(x9033),x9032),f36(x9034,x9033,x9031,f30(f96(x9034,a2)))))
% 1.10/1.34 [885]E(x8851,x8852)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x8853),x8851)),f27(f27(a10,x8854),x8852)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x8853),x8851)),x8854))
% 1.10/1.34 [886]E(x8861,x8862)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x8861),x8863)),f27(f27(a12,x8864),x8862)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x8861),x8863)),x8864))
% 1.10/1.34 [695]E(x6951,x6952)+~E(f27(x6953,x6951),f27(x6953,x6952))+~P14(x6954,x6955,x6953,f30(f96(x6954,a2)))
% 1.10/1.34 [831]E(x8311,x8312)+~E(f36(x8313,x8314,x8315,x8311),f36(x8313,x8314,x8315,x8312))+~P14(x8313,x8314,x8315,f30(f96(x8313,a2)))
% 1.10/1.34 [862]P13(x8621,x8622)+~P13(x8623,x8624)+~P36(f27(f28(f96(x8621,a2),x8622),f36(x8623,x8621,x8625,x8624)))
% 1.10/1.34 [701]~P29(x7011)+P36(f27(f28(x7011,f27(x7012,x7013)),f27(x7014,x7013)))+~P36(f27(f28(f96(x7015,x7011),x7012),x7014))
% 1.10/1.34 [787]P14(x7871,x7872,x7873,x7874)+~P14(x7871,x7872,x7873,x7875)+~P36(f27(f28(f96(x7871,a2),x7874),x7875))
% 1.10/1.34 [813]~P14(x8131,x8132,x8134,x8133)+E(f27(f22(x8131,x8132,x8133,x8134),f27(x8134,x8135)),x8135)+~P36(f27(f27(f34(x8131),x8135),x8133))
% 1.10/1.34 [863]~P14(x8632,x8631,x8634,x8633)+E(f36(x8631,x8632,f22(x8632,x8631,x8633,x8634),f36(x8632,x8631,x8634,x8635)),x8635)+~P36(f27(f28(f96(x8632,a2),x8635),x8633))
% 1.10/1.34 [882]~P14(x8821,x8824,x8825,f30(f96(x8821,a2)))+~P36(f27(f27(f34(x8824),f27(x8825,x8822)),f36(x8821,x8824,x8825,x8823)))+P36(f27(f27(f34(x8821),x8822),x8823))
% 1.10/1.34 [961]~P14(x9611,x9614,x9615,f30(f96(x9611,a2)))+~P36(f27(f28(f96(x9614,a2),f36(x9611,x9614,x9615,x9612)),f36(x9611,x9614,x9615,x9613)))+P36(f27(f28(f96(x9611,a2),x9612),x9613))
% 1.10/1.34 [816]~E(f27(x8163,x8165),x8164)+~P14(x8161,x8162,x8163,f30(f96(x8161,a2)))+E(f27(f22(x8161,x8162,f30(f96(x8161,a2)),x8163),x8164),x8165)
% 1.10/1.34 [940]~P14(x9402,x9401,x9403,x9405)+P36(f27(f27(f29(f96(x9401,a2)),f36(x9402,x9401,x9403,x9404)),f36(x9402,x9401,x9403,x9405)))+~P36(f27(f27(f29(f96(x9402,a2)),x9404),x9405))
% 1.10/1.34 [906]P36(f27(f27(f34(f98(x9061,x9061)),f27(f27(f32(x9061,x9061),x9062),x9063)),f44(x9061,x9064,x9065)))+~P36(f27(f28(a93,f27(x9064,x9062)),f27(x9064,x9063)))+~P36(f27(f27(f34(f98(x9061,x9061)),f27(f27(f32(x9061,x9061),x9062),x9063)),x9065))
% 1.10/1.34 [835]~E(x8352,f27(x8354,x8356))+P36(f27(f27(f34(x8351),x8352),f36(x8353,x8351,x8354,x8355)))+~P36(f27(f27(f34(x8353),x8356),x8355))
% 1.10/1.34 [858]~E(x8582,f36(x8583,x8581,x8584,x8586))+P36(f27(f28(f96(x8581,a2),x8582),f36(x8583,x8581,x8584,x8585)))+~P36(f27(f28(f96(x8583,a2),x8586),x8585))
% 1.10/1.34 [876]~E(f36(x8761,x8762,x8763,x8764),x8766)+E(f36(x8761,x8762,x8763,f36(x8762,x8761,f22(x8761,x8762,x8764,x8763),x8765)),x8765)+~P36(f27(f28(f96(x8762,a2),x8765),x8766))
% 1.10/1.34 [884]~P36(f27(f27(f34(f96(x8845,x8841)),x8842),f17(x8845,x8841,x8846,x8844)))+P36(f27(f27(f34(x8841),f27(x8842,x8843)),f27(x8844,x8843)))+~P36(f27(f27(f34(x8845),x8843),x8846))
% 1.10/1.34 [760]P36(f27(f27(x7601,x7602),x7603))+~P36(f27(f27(x7604,x7602),x7603))+~P36(f27(f28(f96(x7605,f96(x7606,a2)),x7604),x7601))
% 1.10/1.34 [913]P36(f27(f27(f34(x9131),f27(x9132,x9133)),x9134))+~P36(f27(f27(f34(x9135),x9133),x9136))+~P36(f27(f27(f34(f96(x9135,x9131)),x9132),f17(x9135,x9131,x9136,f27(f15(f96(x9131,a2),x9135),x9134))))
% 1.10/1.34 [991]~P13(x9914,x9912)+~P17(x9913,x9914,x9915,x9917,x9916,x9911)+E(f27(x9911,x9912),f18(x9913,x9914,x9915,x9916,x9917,x9912))
% 1.10/1.34 [982]~P36(f27(x9826,x9823))+~P36(f27(f27(f34(f98(x9822,x9822)),f27(f27(f32(x9822,x9822),x9824),x9825)),f27(x9827,x9823)))+P36(f27(f27(f34(f98(f98(x9821,x9822),f98(x9821,x9822))),f27(f27(f32(f98(x9821,x9822),f98(x9821,x9822)),f27(f27(f32(x9821,x9822),x9823),x9824)),f27(f27(f32(x9821,x9822),x9823),x9825))),f33(x9821,x9822,x9826,x9827)))
% 1.10/1.34 [975]~P13(x9752,x9754)+~P16(x9757,x9752,x9755,x9758,x9756,x9751)+E(f27(x9751,f35(x9752,x9753,x9754)),f27(f27(x9755,f27(x9756,x9753)),f27(x9751,x9754)))
% 1.10/1.34 [981]~E(x9813,x9815)+P36(f27(f27(f34(f98(f98(x9811,x9812),f98(x9811,x9812))),f27(f27(f32(f98(x9811,x9812),f98(x9811,x9812)),f27(f27(f32(x9811,x9812),x9813),x9814)),f27(f27(f32(x9811,x9812),x9815),x9816))),f42(x9811,x9812,x9817,x9818)))+~P36(f27(f27(f34(f98(x9812,x9812)),f27(f27(f32(x9812,x9812),x9814),x9816)),x9818))
% 1.10/1.34 [990]E(x9901,x9902)+~P36(f27(f27(f34(f98(f98(x9903,x9905),f98(x9903,x9905))),f27(f27(f32(f98(x9903,x9905),f98(x9903,x9905)),f27(f27(f32(x9903,x9905),x9901),x9906)),f27(f27(f32(x9903,x9905),x9902),x9907))),f42(x9903,x9905,x9904,x9908)))+P36(f27(f27(f34(f98(x9903,x9903)),f27(f27(f32(x9903,x9903),x9901),x9902)),x9904))
% 1.10/1.34 [996]~P36(f27(f27(f34(f98(f98(x9961,x9965),f98(x9961,x9965))),f27(f27(f32(f98(x9961,x9965),f98(x9961,x9965)),f27(f27(f32(x9961,x9965),x9962),x9966)),f27(f27(f32(x9961,x9965),x9963),x9967))),f42(x9961,x9965,x9964,x9968)))+P36(f27(f27(f34(f98(x9961,x9961)),f27(f27(f32(x9961,x9961),x9962),x9963)),x9964))+P36(f27(f27(f34(f98(x9965,x9965)),f27(f27(f32(x9965,x9965),x9966),x9967)),x9968))
% 1.10/1.34 [894]E(f27(a99,x8941),a108)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(a104,x8941)))+P36(f27(f27(f29(a93),f27(a99,x8941)),a108))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(f27(a12,f27(a104,x8941)),a107)))
% 1.10/1.34 [902]E(f27(a99,x9021),a108)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(a104,x9021)))+P36(f27(f27(f29(a93),f27(a99,x9021)),a108))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(f27(a12,f27(a104,x9021)),a107)))
% 1.10/1.34 [945]E(f27(a99,x9451),a108)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(a104,x9451)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(f27(a12,f27(a104,x9451)),a107)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(f27(a10,f27(a104,x9451)),a107)))
% 1.10/1.34 [905]~E(f27(a99,x9051),a108)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(a104,x9051)))+P36(f27(f27(f29(a93),f27(a99,x9051)),a108))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(f27(f27(a11,f27(a104,x9051)),a105),a107)))
% 1.10/1.34 [916]~E(f27(a99,x9161),a108)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(a104,x9161)))+P36(f27(f27(f29(a93),f27(a99,x9161)),a108))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(f27(f27(a11,f27(a104,x9161)),a105),a107)))
% 1.10/1.34 [957]~E(f27(a99,x9571),a108)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(a104,x9571)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(f27(a10,f27(a104,x9571)),a107)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(f27(f27(a11,f27(a104,x9571)),a105),a107)))
% 1.10/1.34 [959]P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(a104,x9591)))+P36(f27(f27(f29(a93),f27(a99,x9591)),a108))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(f27(a12,f27(a104,x9591)),a107)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(f27(f27(a11,f27(a104,x9591)),a105),a107)))
% 1.10/1.34 [969]P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(a104,x9691)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(f27(a12,f27(a104,x9691)),a107)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(f27(a10,f27(a104,x9691)),a107)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),a105),a106)),f27(f27(f27(a11,f27(a104,x9691)),a105),a107)))
% 1.10/1.34 [901]~P32(x9011)+~P36(f27(f27(f34(x9011),x9012),f24(x9011)))+P36(f27(f27(f29(x9011),f27(f27(f19(x9011),f27(f27(f19(x9011),f4(x9011)),x9012)),x9012)),f3(x9011)))+~P36(f27(f27(f29(x9011),x9012),f3(x9011)))
% 1.10/1.34 [943]~P32(x9431)+~P36(f27(f27(f34(x9431),x9432),f24(x9431)))+~P36(f27(f27(f29(x9431),f27(f27(f19(x9431),f27(f27(f19(x9431),f4(x9431)),x9432)),x9432)),f3(x9431)))+P36(f27(f27(f29(x9431),x9432),f3(x9431)))
% 1.10/1.34 [575]~P27(x5751)+~E(x5752,f3(x5751))+E(f27(f27(f19(x5751),x5752),x5752),f3(x5751))+~P36(f27(f27(f34(x5751),x5752),f24(x5751)))
% 1.10/1.34 [590]~P27(x5902)+E(x5901,f3(x5902))+~E(f27(f27(f19(x5902),x5901),x5901),f3(x5902))+~P36(f27(f27(f34(x5902),x5901),f24(x5902)))
% 1.10/1.34 [584]E(x5841,x5842)+~P28(x5843)+~P36(f27(f28(x5843,x5842),x5841))+~P36(f27(f28(x5843,x5841),x5842))
% 1.10/1.34 [623]~P36(f27(x6231,x6232))+~P36(f27(x6231,x6233))+~P36(f27(f28(a93,x6233),f72(x6232,x6231)))+P36(f27(x6231,f3(a93)))
% 1.10/1.34 [764]~P26(x7641)+~P36(f27(f28(x7641,x7643),f3(x7641)))+~P36(f27(f28(x7641,x7642),f3(x7641)))+P36(f27(f28(x7641,f27(f27(f19(x7641),x7642),x7643)),f3(x7641)))
% 1.10/1.34 [775]~P26(x7751)+~P36(f27(f28(x7751,x7753),f3(x7751)))+~P36(f27(f27(f29(x7751),x7752),f3(x7751)))+P36(f27(f27(f29(x7751),f27(f27(f19(x7751),x7752),x7753)),f3(x7751)))
% 1.10/1.34 [776]~P26(x7761)+~P36(f27(f28(x7761,x7762),f3(x7761)))+~P36(f27(f27(f29(x7761),x7763),f3(x7761)))+P36(f27(f27(f29(x7761),f27(f27(f19(x7761),x7762),x7763)),f3(x7761)))
% 1.10/1.34 [784]~P34(x7841)+~P36(f27(f27(f34(x7841),x7843),f24(x7841)))+~P36(f27(f27(f34(x7841),x7842),f24(x7841)))+P36(f27(f27(f34(x7841),f27(f27(f19(x7841),x7842),x7843)),f24(x7841)))
% 1.10/1.34 [785]~P26(x7851)+~P36(f27(f27(f29(x7851),x7853),f3(x7851)))+~P36(f27(f27(f29(x7851),x7852),f3(x7851)))+P36(f27(f27(f29(x7851),f27(f27(f19(x7851),x7852),x7853)),f3(x7851)))
% 1.10/1.34 [527]~E(x5272,x5273)+~P6(x5271)+P36(f27(f28(x5271,x5272),x5273))+P36(f27(f27(f29(x5271),x5272),x5273))
% 1.10/1.34 [541]~P32(x5413)+E(x5411,x5412)+P36(f27(f27(f29(x5413),x5412),x5411))+P36(f27(f27(f29(x5413),x5411),x5412))
% 1.10/1.34 [542]~P6(x5423)+E(x5421,x5422)+P36(f27(f27(f29(x5423),x5422),x5421))+P36(f27(f27(f29(x5423),x5421),x5422))
% 1.10/1.34 [558]~P28(x5583)+E(x5581,x5582)+~P36(f27(f28(x5583,x5582),x5581))+P36(f27(f27(f29(x5583),x5582),x5581))
% 1.10/1.34 [560]~P6(x5603)+E(x5601,x5602)+~P36(f27(f28(x5603,x5601),x5602))+P36(f27(f27(f29(x5603),x5601),x5602))
% 1.10/1.34 [566]~P28(x5663)+E(x5661,x5662)+~P36(f27(f28(x5663,x5661),x5662))+P36(f27(f27(f29(x5663),x5661),x5662))
% 1.10/1.34 [620]~P5(x6201)+~P36(f27(f28(x6201,x6203),x6202))+P36(f27(f28(x6201,x6202),x6203))+P36(f27(f27(f29(x6201),x6203),x6202))
% 1.10/1.34 [728]E(x7281,x7282)+~P13(x7283,x7281)+~P36(f27(f28(a93,f14(x7283,x7281)),f14(x7283,x7282)))+~P36(f27(f28(f96(x7283,a2),x7282),x7281))
% 1.10/1.34 [938]~P13(x9381,x9383)+~P14(x9381,x9381,x9382,x9383)+E(f36(x9381,x9381,x9382,x9383),x9383)+~P36(f27(f28(f96(x9381,a2),f36(x9381,x9381,x9382,x9383)),x9383))
% 1.10/1.34 [747]~P26(x7471)+~P36(f27(f27(f29(x7471),f3(x7471)),x7473))+~P36(f27(f27(f29(x7471),f3(x7471)),x7472))+P36(f27(f27(f29(x7471),f3(x7471)),f27(f27(f19(x7471),x7472),x7473)))
% 1.10/1.34 [794]~P13(x7941,x7943)+~P36(f27(f27(f29(a93),f14(x7941,x7942)),f14(x7941,x7943)))+~P36(f27(f28(f96(x7941,a2),x7942),x7943))+P36(f27(f27(f29(f96(x7941,a2)),x7942),x7943))
% 1.10/1.34 [891]E(x8911,x8912)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x8911),x8912)),x8913))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x8912),x8911)),x8913))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x8913),a7))
% 1.10/1.34 [634]~P28(x6341)+~P36(f27(f28(x6341,x6344),x6343))+P36(f27(f28(x6341,x6342),x6343))+~P36(f27(f28(x6341,x6342),x6344))
% 1.10/1.34 [635]~P5(x6351)+~P36(f27(f28(x6351,x6352),x6354))+P36(f27(f28(x6351,x6352),x6353))+~P36(f27(f28(x6351,x6354),x6353))
% 1.10/1.34 [820]~P13(x8202,x8203)+~P13(x8201,x8204)+P14(x8201,x8202,f82(x8203,x8202,x8204,x8201),x8204)+~P36(f27(f28(a93,f14(x8201,x8204)),f14(x8202,x8203)))
% 1.10/1.34 [653]E(x6531,x6532)+~E(f35(x6533,x6534,x6531),f35(x6533,x6534,x6532))+P36(f27(f27(f34(x6533),x6534),x6532))+P36(f27(f27(f34(x6533),x6534),x6531))
% 1.10/1.34 [657]~P28(x6571)+~P36(f27(f28(x6571,x6572),x6574))+~P36(f27(f27(f29(x6571),x6574),x6573))+P36(f27(f27(f29(x6571),x6572),x6573))
% 1.10/1.34 [658]~P28(x6581)+~P36(f27(f28(x6581,x6584),x6583))+~P36(f27(f27(f29(x6581),x6582),x6584))+P36(f27(f27(f29(x6581),x6582),x6583))
% 1.10/1.34 [659]~P5(x6591)+~P36(f27(f28(x6591,x6594),x6593))+~P36(f27(f27(f29(x6591),x6592),x6594))+P36(f27(f27(f29(x6591),x6592),x6593))
% 1.10/1.34 [660]~P5(x6601)+~P36(f27(f28(x6601,x6602),x6604))+~P36(f27(f27(f29(x6601),x6604),x6603))+P36(f27(f27(f29(x6601),x6602),x6603))
% 1.10/1.34 [675]~P28(x6751)+~P36(f27(f27(f29(x6751),x6754),x6753))+P36(f27(f27(f29(x6751),x6752),x6753))+~P36(f27(f27(f29(x6751),x6752),x6754))
% 1.10/1.34 [676]~P5(x6761)+~P36(f27(f27(f29(x6761),x6762),x6764))+P36(f27(f27(f29(x6761),x6762),x6763))+~P36(f27(f27(f29(x6761),x6764),x6763))
% 1.10/1.34 [804]~E(x8043,x8041)+E(x8041,x8042)+E(x8043,x8042)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x8042),x8043)),f27(f27(a10,x8044),x8041)))
% 1.10/1.34 [805]~E(x8053,x8051)+E(x8051,x8052)+E(x8053,x8052)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x8053),x8052)),f27(f27(a12,x8054),x8051)))
% 1.10/1.34 [715]~P26(x7151)+~P36(f27(f28(x7151,x7152),x7153))+~P36(f27(f28(x7151,f3(x7151)),x7154))+P36(f27(f28(x7151,x7152),f27(f27(f19(x7151),x7153),x7154)))
% 1.10/1.34 [716]~P26(x7161)+~P36(f27(f28(x7161,x7162),x7164))+~P36(f27(f28(x7161,f3(x7161)),x7163))+P36(f27(f28(x7161,x7162),f27(f27(f19(x7161),x7163),x7164)))
% 1.10/1.34 [724]~P26(x7241)+~P36(f27(f28(x7241,x7242),x7244))+~P36(f27(f27(f29(x7241),f3(x7241)),x7243))+P36(f27(f27(f29(x7241),x7242),f27(f27(f19(x7241),x7243),x7244)))
% 1.10/1.34 [725]~P26(x7251)+~P36(f27(f28(x7251,f3(x7251)),x7253))+~P36(f27(f27(f29(x7251),x7252),x7254))+P36(f27(f27(f29(x7251),x7252),f27(f27(f19(x7251),x7253),x7254)))
% 1.10/1.34 [734]~P30(x7341)+~P36(f27(f27(f29(x7341),f3(x7341)),x7343))+~P36(f27(f27(f29(x7341),x7342),x7344))+P36(f27(f27(f29(x7341),x7342),f27(f27(f19(x7341),x7343),x7344)))
% 1.10/1.34 [762]~P29(x7622)+~P36(f27(f28(f96(x7621,x7622),x7624),x7623))+P36(f27(f28(f96(x7621,x7622),x7623),x7624))+P36(f27(f27(f29(f96(x7621,x7622)),x7624),x7623))
% 1.10/1.34 [967]~P13(x9672,x9674)+~P13(x9671,x9673)+~P36(f27(f28(a93,f14(x9672,x9674)),f14(x9671,x9673)))+P36(f27(f28(f96(x9671,a2),f36(x9672,x9671,f82(x9673,x9671,x9674,x9672),x9674)),x9673))
% 1.10/1.34 [877]E(x8771,x8772)+E(x8773,x8772)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x8773),x8771)),f27(f27(a10,x8774),x8772)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x8773),x8771)),x8774))
% 1.10/1.34 [878]E(x8781,x8782)+E(x8783,x8782)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x8783),x8781)),f27(f27(a12,x8784),x8782)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x8783),x8781)),x8784))
% 1.10/1.34 [879]E(x8791,x8792)+E(x8793,x8791)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x8793),x8791)),f27(f27(a12,x8794),x8792)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x8793),x8791)),x8794))
% 1.10/1.34 [880]E(x8801,x8802)+E(x8801,x8803)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x8801),x8803)),f27(f27(a10,x8804),x8802)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x8801),x8803)),x8804))
% 1.10/1.34 [972]~P2(x9723)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9721),x9722)),f27(x9723,x9724)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9721),x9722)),f27(x9724,f55(x9723,x9724,x9721,x9722))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x9724),a8))
% 1.10/1.34 [844]~P6(x8441)+P36(f27(f28(x8441,x8442),x8443))+P36(f27(f28(x8441,x8444),x8443))+~P36(f27(f28(f96(x8441,a2),f31(x8441,x8443,x8442)),f31(x8441,x8444,x8445)))
% 1.10/1.34 [845]~P6(x8451)+P36(f27(f28(x8451,x8452),x8453))+P36(f27(f28(x8451,x8452),x8454))+~P36(f27(f28(f96(x8451,a2),f31(x8451,x8453,x8452)),f31(x8451,x8455,x8454)))
% 1.10/1.34 [937]~P13(x9373,x9374)+~P14(x9371,x9373,x9375,x9372)+P36(f27(f28(a93,f14(x9371,x9372)),f14(x9373,x9374)))+~P36(f27(f28(f96(x9373,a2),f36(x9371,x9373,x9375,x9372)),x9374))
% 1.10/1.34 [793]~P24(x7931)+~P36(f27(f28(x7931,x7933),x7935))+~P36(f27(f28(x7931,x7932),x7934))+P36(f27(f28(x7931,f27(f27(f19(x7931),x7932),x7933)),f27(f27(f19(x7931),x7934),x7935)))
% 1.10/1.34 [799]~P7(x7991)+~P36(f27(f28(x7991,x7993),x7995))+~P36(f27(f27(f29(x7991),x7992),x7994))+P36(f27(f27(f29(x7991),f27(f27(f19(x7991),x7992),x7993)),f27(f27(f19(x7991),x7994),x7995)))
% 1.10/1.34 [800]~P7(x8001)+~P36(f27(f28(x8001,x8002),x8004))+~P36(f27(f27(f29(x8001),x8003),x8005))+P36(f27(f27(f29(x8001),f27(f27(f19(x8001),x8002),x8003)),f27(f27(f19(x8001),x8004),x8005)))
% 1.10/1.34 [807]~P7(x8071)+~P36(f27(f27(f29(x8071),x8073),x8075))+~P36(f27(f27(f29(x8071),x8072),x8074))+P36(f27(f27(f29(x8071),f27(f27(f19(x8071),x8072),x8073)),f27(f27(f19(x8071),x8074),x8075)))
% 1.10/1.34 [893]~E(x8932,f27(x8933,x8931))+E(x8931,f76(x8932,x8933,x8934,x8935))+~P14(x8935,x8934,x8933,f30(f96(x8935,a2)))+~P36(f27(f27(f34(x8934),x8932),f36(x8935,x8934,x8933,f30(f96(x8935,a2)))))
% 1.10/1.34 [890]E(x8901,x8902)+~E(x8903,x8904)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x8903),x8904)),f13(x8905,x8901,x8902)))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x8905),a7))
% 1.10/1.34 [899]E(x8991,x8992)+~E(x8993,x8994)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x8993),x8994)),f27(f27(f27(a11,x8995),x8991),x8992)))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x8995),a7))
% 1.10/1.34 [929]~P13(x9293,x9294)+~P14(x9291,x9293,x9295,x9292)+P36(f27(f28(a93,f14(x9291,x9292)),f14(x9293,x9294)))+~P36(f27(f27(f34(f96(x9291,x9293)),x9295),f17(x9291,x9293,x9292,f27(f15(f96(x9293,a2),x9291),x9294))))
% 1.10/1.34 [955]E(x9551,x9552)+~E(f27(f22(x9553,x9554,x9555,x9556),x9551),f27(f22(x9553,x9554,x9555,x9556),x9552))+~P36(f27(f27(f34(x9554),x9552),f36(x9553,x9554,x9556,x9555)))+~P36(f27(f27(f34(x9554),x9551),f36(x9553,x9554,x9556,x9555)))
% 1.10/1.34 [812]~P14(x8121,x8122,x8124,x8123)+~E(f27(x8124,x8126),x8125)+E(f27(f22(x8121,x8122,x8123,x8124),x8125),x8126)+~P36(f27(f27(f34(x8121),x8126),x8123))
% 1.10/1.34 [976]~P16(x9767,x9766,x9761,x9768,x9762,x9764)+~P13(x9766,x9765)+E(f27(f27(x9761,f27(x9762,x9763)),f27(x9764,x9765)),f27(x9764,x9765))+~P36(f27(f27(f34(x9766),x9763),x9765))
% 1.10/1.34 [977]~P13(x9772,x9774)+~P17(x9777,x9772,x9775,x9778,x9776,x9771)+E(f27(x9771,f35(x9772,x9773,x9774)),f27(f27(x9775,f27(x9776,x9773)),f27(x9771,x9774)))+P36(f27(f27(f34(x9772),x9773),x9774))
% 1.10/1.34 [978]~P16(x9786,x9785,x9781,x9787,x9788,x9782)+~P13(x9785,x9784)+E(f27(f27(x9781,f27(x9782,x9783)),f27(x9782,x9784)),f27(x9782,x9784))+~P36(f27(f28(f96(x9785,a2),x9783),x9784))
% 1.10/1.34 [673]~P26(x6732)+E(x6731,f3(x6732))+~E(f27(f27(f19(x6732),x6733),x6731),f3(x6732))+~P36(f27(f28(x6732,f3(x6732)),x6733))+~P36(f27(f28(x6732,f3(x6732)),x6731))
% 1.10/1.34 [674]~P26(x6742)+E(x6741,f3(x6742))+~E(f27(f27(f19(x6742),x6741),x6743),f3(x6742))+~P36(f27(f28(x6742,f3(x6742)),x6743))+~P36(f27(f28(x6742,f3(x6742)),x6741))
% 1.10/1.34 [692]~P6(x6923)+E(x6921,x6922)+~E(f31(x6923,x6924,x6921),f31(x6923,x6925,x6922))+~P36(f27(f27(f29(x6923),x6925),x6922))+~P36(f27(f27(f29(x6923),x6924),x6921))
% 1.10/1.34 [693]~P6(x6933)+E(x6931,x6932)+~E(f31(x6933,x6931,x6934),f31(x6933,x6932,x6935))+~P36(f27(f27(f29(x6933),x6932),x6935))+~P36(f27(f27(f29(x6933),x6931),x6934))
% 1.10/1.34 [917]E(x9171,x9172)+~E(x9175,x9171)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9173),x9175)),f13(x9174,x9171,x9172)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9173),x9172)),x9174))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9174),a7))
% 1.10/1.34 [932]E(x9321,x9322)+~E(x9325,x9321)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9325),x9323)),f27(f27(f27(a11,x9324),x9322),x9321)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9322),x9323)),x9324))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9324),a7))
% 1.10/1.34 [756]E(x7561,x7562)+~P14(x7564,x7565,x7563,x7566)+~E(f27(x7563,x7561),f27(x7563,x7562))+~P36(f27(f27(f34(x7564),x7562),x7566))+~P36(f27(f27(f34(x7564),x7561),x7566))
% 1.10/1.34 [663]~P26(x6631)+~E(x6633,f3(x6631))+~E(x6632,f3(x6631))+E(f27(f27(f19(x6631),x6632),x6633),f3(x6631))+~P36(f27(f28(x6631,f3(x6631)),x6633))+~P36(f27(f28(x6631,f3(x6631)),x6632))
% 1.10/1.34 [985]~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9851),x9852)),f27(a1,x9854)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9851),x9852)),f27(a1,x9853)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9851),x9852)),f27(x9854,f69(x9853,x9854,x9851,x9852))))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9851),x9852)),f27(x9853,f69(x9853,x9854,x9851,x9852))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x9853),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x9854),a8))
% 1.10/1.34 [986]~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9861),x9862)),f27(a1,x9864)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9861),x9862)),f27(a1,x9863)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9861),x9862)),f27(x9864,f69(x9864,x9863,x9861,x9862))))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9861),x9862)),f27(x9863,f69(x9864,x9863,x9861,x9862))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x9863),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x9864),a8))
% 1.10/1.34 [992]~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9921),x9922)),f27(a1,x9924)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9921),x9922)),f27(a1,x9923)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9921),x9922)),f27(x9924,f69(x9923,x9924,x9921,x9922))))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9921),x9922)),f27(x9923,f69(x9923,x9924,x9921,x9922))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x9923),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x9924),a8))
% 1.10/1.34 [993]~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9931),x9932)),f27(a1,x9934)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9931),x9932)),f27(a1,x9933)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9931),x9932)),f27(x9934,f69(x9934,x9933,x9931,x9932))))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9931),x9932)),f27(x9933,f69(x9934,x9933,x9931,x9932))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x9933),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x9934),a8))
% 1.10/1.34 [908]~E(x9083,x9081)+E(x9081,x9082)+E(x9083,x9084)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9084),x9083)),f13(x9085,x9081,x9082)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9084),x9082)),x9085))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9085),a7))
% 1.10/1.34 [918]E(x9181,x9182)+E(x9181,x9183)+E(x9184,x9181)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9184),x9183)),f13(x9185,x9181,x9182)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9184),x9183)),x9185))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9185),a7))
% 1.10/1.34 [921]~E(x9213,x9211)+E(x9211,x9212)+E(x9213,x9214)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9213),x9214)),f27(f27(f27(a11,x9215),x9212),x9211)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9212),x9214)),x9215))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9215),a7))
% 1.10/1.34 [933]E(x9331,x9332)+E(x9331,x9333)+E(x9334,x9331)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9333),x9334)),f27(f27(f27(a11,x9335),x9332),x9331)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9333),x9334)),x9335))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9335),a7))
% 1.10/1.34 [987]E(x9871,x9872)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9871),x9872)),f27(a1,x9874)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9872),x9871)),f27(a1,x9873)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9872),x9871)),f27(x9873,f85(x9873,x9874,x9872,x9871))))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9871),x9872)),f27(x9874,f85(x9873,x9874,x9872,x9871))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x9873),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x9874),a8))
% 1.10/1.34 [988]E(x9881,x9882)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9881),x9882)),f27(a1,x9884)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9882),x9881)),f27(a1,x9883)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9882),x9881)),f27(x9883,f85(x9884,x9883,x9881,x9882))))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9881),x9882)),f27(x9884,f85(x9884,x9883,x9881,x9882))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x9883),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x9884),a8))
% 1.10/1.34 [994]E(x9941,x9942)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9941),x9942)),f27(a1,x9944)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9942),x9941)),f27(a1,x9943)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9942),x9941)),f27(x9943,f85(x9943,x9944,x9942,x9941))))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9941),x9942)),f27(x9944,f85(x9943,x9944,x9942,x9941))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x9943),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x9944),a8))
% 1.10/1.34 [995]E(x9951,x9952)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9951),x9952)),f27(a1,x9954)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9952),x9951)),f27(a1,x9953)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9952),x9951)),f27(x9953,f85(x9954,x9953,x9951,x9952))))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9951),x9952)),f27(x9954,f85(x9954,x9953,x9951,x9952))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x9953),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x9954),a8))
% 1.10/1.34 [867]~E(x8673,x8672)+~E(x8674,x8671)+E(x8671,x8672)+E(x8671,x8673)+E(x8674,x8673)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x8674),x8673)),f13(x8675,x8671,x8672)))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x8675),a7))
% 1.10/1.34 [870]~E(x8703,x8702)+~E(x8704,x8701)+E(x8701,x8702)+E(x8701,x8703)+E(x8704,x8703)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x8703),x8704)),f27(f27(f27(a11,x8705),x8702),x8701)))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x8705),a7))
% 1.10/1.34 [909]E(x9094,x9093)+E(x9091,x9092)+E(x9093,x9091)+E(x9094,x9091)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9094),x9093)),f13(x9095,x9091,x9092)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9094),x9093)),x9095))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9095),a7))
% 1.10/1.34 [910]~E(x9103,x9101)+E(x9101,x9102)+E(x9103,x9102)+E(x9104,x9103)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9104),x9103)),f13(x9105,x9102,x9101)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9104),x9103)),x9105))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9105),a7))
% 1.10/1.34 [911]~E(x9114,x9111)+E(x9111,x9112)+E(x9111,x9113)+E(x9114,x9112)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9114),x9112)),f13(x9115,x9111,x9113)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9113),x9112)),x9115))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9115),a7))
% 1.10/1.34 [912]~E(x9124,x9122)+~E(x9123,x9121)+E(x9121,x9122)+E(x9123,x9124)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9123),x9124)),f13(x9125,x9121,x9122)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9123),x9122)),x9125))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9125),a7))
% 1.10/1.34 [920]E(x9203,x9201)+E(x9201,x9202)+E(x9203,x9202)+~E(x9205,x9203)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9205),x9201)),f13(x9204,x9203,x9202)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9202),x9201)),x9204))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9204),a7))
% 1.10/1.34 [922]E(x9224,x9223)+E(x9221,x9222)+E(x9223,x9221)+E(x9224,x9221)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9224),x9223)),f27(f27(f27(a11,x9225),x9222),x9221)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9224),x9223)),x9225))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9225),a7))
% 1.10/1.34 [923]~E(x9233,x9231)+E(x9231,x9232)+E(x9233,x9232)+E(x9233,x9234)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9233),x9234)),f27(f27(f27(a11,x9235),x9231),x9232)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9233),x9234)),x9235))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9235),a7))
% 1.10/1.34 [924]~E(x9244,x9241)+E(x9241,x9242)+E(x9241,x9243)+E(x9244,x9243)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9243),x9244)),f27(f27(f27(a11,x9245),x9242),x9241)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9243),x9242)),x9245))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9245),a7))
% 1.10/1.34 [925]~E(x9254,x9252)+~E(x9253,x9251)+E(x9251,x9252)+E(x9253,x9254)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9254),x9253)),f27(f27(f27(a11,x9255),x9252),x9251)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9252),x9253)),x9255))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9255),a7))
% 1.10/1.34 [934]E(x9343,x9341)+E(x9341,x9342)+E(x9343,x9342)+~E(x9345,x9343)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9341),x9345)),f27(f27(f27(a11,x9344),x9342),x9343)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9341),x9342)),x9344))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9344),a7))
% 1.10/1.34 [947]E(x9471,x9472)+E(x9473,x9472)+E(x9474,x9473)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9474),x9473)),f13(x9475,x9472,x9471)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9474),x9473)),x9475))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9471),x9473)),x9475))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9475),a7))
% 1.10/1.34 [948]E(x9481,x9482)+E(x9483,x9481)+E(x9483,x9484)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9483),x9484)),f13(x9485,x9481,x9482)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9483),x9484)),x9485))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9483),x9482)),x9485))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9485),a7))
% 1.10/1.34 [949]~E(x9494,x9491)+E(x9491,x9492)+E(x9493,x9494)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9493),x9494)),f13(x9495,x9492,x9491)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9493),x9494)),x9495))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9493),x9491)),x9495))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9495),a7))
% 1.10/1.34 [950]~E(x9503,x9501)+E(x9501,x9502)+E(x9503,x9504)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9503),x9504)),f13(x9505,x9501,x9502)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9502),x9504)),x9505))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9503),x9502)),x9505))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9505),a7))
% 1.10/1.34 [951]E(x9511,x9512)+E(x9513,x9511)+E(x9514,x9513)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9514),x9513)),f27(f27(f27(a11,x9515),x9512),x9511)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9514),x9513)),x9515))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9512),x9513)),x9515))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9515),a7))
% 1.10/1.34 [952]E(x9521,x9522)+E(x9523,x9522)+E(x9523,x9524)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9523),x9524)),f27(f27(f27(a11,x9525),x9521),x9522)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9523),x9524)),x9525))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9523),x9521)),x9525))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9525),a7))
% 1.10/1.34 [953]~E(x9533,x9531)+E(x9531,x9532)+E(x9533,x9534)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9533),x9534)),f27(f27(f27(a11,x9535),x9531),x9532)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9533),x9534)),x9535))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9531),x9534)),x9535))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9535),a7))
% 1.10/1.34 [954]~E(x9543,x9541)+E(x9541,x9542)+E(x9543,x9544)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9544),x9543)),f27(f27(f27(a11,x9545),x9542),x9541)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9542),x9543)),x9545))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9544),x9542)),x9545))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9545),a7))
% 1.10/1.34 [965]E(x9651,x9652)+E(x9653,x9654)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9653),x9654)),f13(x9655,x9652,x9651)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9653),x9654)),x9655))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9651),x9654)),x9655))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9653),x9651)),x9655))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9655),a7))
% 1.10/1.34 [966]E(x9661,x9662)+E(x9663,x9664)+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9663),x9664)),f27(f27(f27(a11,x9665),x9661),x9662)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9663),x9664)),x9665))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9661),x9664)),x9665))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x9663),x9661)),x9665))+~P36(f27(f27(f34(f96(f98(a92,a92),a2)),x9665),a7))
% 1.10/1.34 [1003]~P1(x10033)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10031),x10032)),f27(x10033,x10035)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10031),x10032)),f27(x10033,x10034)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10031),x10032)),f27(x10035,f88(x10033,x10034,x10035,x10031,x10032))))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10031),x10032)),f27(x10034,f88(x10033,x10034,x10035,x10031,x10032))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10034),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10035),a8))
% 1.10/1.34 [1004]~P1(x10043)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10041),x10042)),f27(x10043,x10045)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10041),x10042)),f27(x10043,x10044)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10041),x10042)),f27(x10045,f88(x10043,x10045,x10044,x10041,x10042))))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10041),x10042)),f27(x10044,f88(x10043,x10045,x10044,x10041,x10042))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10044),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10045),a8))
% 1.10/1.34 [1007]~P1(x10073)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10071),x10072)),f27(x10073,x10075)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10071),x10072)),f27(x10073,x10074)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10071),x10072)),f27(x10075,f88(x10073,x10074,x10075,x10071,x10072))))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10071),x10072)),f27(x10074,f88(x10073,x10074,x10075,x10071,x10072))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10074),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10075),a8))
% 1.10/1.34 [1008]~P1(x10083)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10081),x10082)),f27(x10083,x10085)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10081),x10082)),f27(x10083,x10084)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10081),x10082)),f27(x10085,f88(x10083,x10085,x10084,x10081,x10082))))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10081),x10082)),f27(x10084,f88(x10083,x10085,x10084,x10081,x10082))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10084),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10085),a8))
% 1.10/1.34 [973]~P13(x9733,x9734)+~P13(x9731,x9732)+~P14(x9733,x9731,x9735,x9734)+~P14(x9731,x9733,x9736,x9732)+E(f14(x9731,x9732),f14(x9733,x9734))+~P36(f27(f28(f96(x9733,a2),f36(x9731,x9733,x9736,x9732)),x9734))+~P36(f27(f28(f96(x9731,a2),f36(x9733,x9731,x9735,x9734)),x9732))
% 1.10/1.34 [971]~P13(x9713,x9714)+~P13(x9711,x9712)+~P14(x9713,x9711,x9715,x9714)+~P14(x9711,x9713,x9716,x9712)+E(f14(x9711,x9712),f14(x9713,x9714))+~P36(f27(f27(f34(f96(x9713,x9711)),x9715),f17(x9713,x9711,x9714,f27(f15(f96(x9711,a2),x9713),x9712))))+~P36(f27(f27(f34(f96(x9711,x9713)),x9716),f17(x9711,x9713,x9712,f27(f15(f96(x9713,a2),x9711),x9714))))
% 1.10/1.34 [1012]E(x10121,x10122)+E(x10123,x10124)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10123),x10124)),f27(a1,x10126)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10121),x10122)),f27(a1,x10125)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10121),x10122)),f27(x10125,f87(x10125,x10126,x10122,x10121,x10124,x10123))))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10123),x10124)),f27(x10126,f87(x10125,x10126,x10122,x10121,x10124,x10123))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10125),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10126),a8))
% 1.10/1.34 [1013]E(x10131,x10132)+E(x10133,x10134)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10133),x10134)),f27(a1,x10136)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10131),x10132)),f27(a1,x10135)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10131),x10132)),f27(x10135,f87(x10136,x10135,x10134,x10133,x10132,x10131))))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10133),x10134)),f27(x10136,f87(x10136,x10135,x10134,x10133,x10132,x10131))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10135),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10136),a8))
% 1.10/1.34 [1019]E(x10191,x10192)+E(x10193,x10194)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10193),x10194)),f27(a1,x10196)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10191),x10192)),f27(a1,x10195)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10191),x10192)),f27(x10195,f87(x10195,x10196,x10192,x10191,x10194,x10193))))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10193),x10194)),f27(x10196,f87(x10195,x10196,x10192,x10191,x10194,x10193))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10195),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10196),a8))
% 1.10/1.34 [1020]E(x10201,x10202)+E(x10203,x10204)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10203),x10204)),f27(a1,x10206)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10201),x10202)),f27(a1,x10205)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10201),x10202)),f27(x10205,f87(x10206,x10205,x10204,x10203,x10202,x10201))))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10203),x10204)),f27(x10206,f87(x10206,x10205,x10204,x10203,x10202,x10201))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10205),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10206),a8))
% 1.10/1.34 [1001]E(x10013,x10011)+E(x10011,x10012)+E(x10013,x10012)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10013),x10011)),f27(a1,x10015)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10012),x10013)),f27(a1,x10014)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10012),x10013)),f27(x10014,f86(x10015,x10014,x10011,x10013,x10012))))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10013),x10011)),f27(x10015,f86(x10015,x10014,x10011,x10013,x10012))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10014),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10015),a8))
% 1.10/1.34 [1002]E(x10023,x10021)+E(x10021,x10022)+E(x10023,x10022)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10023),x10021)),f27(a1,x10025)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10021),x10022)),f27(a1,x10024)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10021),x10022)),f27(x10024,f86(x10024,x10025,x10022,x10021,x10023))))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10023),x10021)),f27(x10025,f86(x10024,x10025,x10022,x10021,x10023))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10024),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10025),a8))
% 1.10/1.34 [1005]E(x10053,x10051)+E(x10051,x10052)+E(x10053,x10052)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10053),x10051)),f27(a1,x10055)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10052),x10053)),f27(a1,x10054)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10052),x10053)),f27(x10054,f86(x10055,x10054,x10051,x10053,x10052))))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10053),x10051)),f27(x10055,f86(x10055,x10054,x10051,x10053,x10052))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10054),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10055),a8))
% 1.10/1.34 [1006]E(x10063,x10061)+E(x10061,x10062)+E(x10063,x10062)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10063),x10061)),f27(a1,x10065)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10061),x10062)),f27(a1,x10064)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10061),x10062)),f27(x10064,f86(x10064,x10065,x10062,x10061,x10063))))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10063),x10061)),f27(x10065,f86(x10064,x10065,x10062,x10061,x10063))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10064),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10065),a8))
% 1.10/1.34 [1014]E(x10144,x10143)+E(x10141,x10142)+E(x10143,x10142)+E(x10144,x10141)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10144),x10143)),f27(a1,x10146)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10142),x10141)),f27(a1,x10145)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10142),x10141)),f27(x10145,f89(x10145,x10146,x10141,x10142,x10143,x10144))))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10144),x10143)),f27(x10146,f89(x10145,x10146,x10141,x10142,x10143,x10144))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10145),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10146),a8))
% 1.10/1.34 [1015]E(x10154,x10153)+E(x10151,x10152)+E(x10153,x10151)+E(x10154,x10152)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10154),x10153)),f27(a1,x10156)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10151),x10152)),f27(a1,x10155)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10151),x10152)),f27(x10155,f90(x10155,x10156,x10152,x10151,x10153,x10154))))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10154),x10153)),f27(x10156,f90(x10155,x10156,x10152,x10151,x10153,x10154))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10155),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10156),a8))
% 1.10/1.34 [1016]E(x10164,x10163)+E(x10161,x10162)+E(x10163,x10161)+E(x10164,x10162)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10164),x10163)),f27(a1,x10166)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10161),x10162)),f27(a1,x10165)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10161),x10162)),f27(x10165,f90(x10166,x10165,x10163,x10164,x10162,x10161))))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10164),x10163)),f27(x10166,f90(x10166,x10165,x10163,x10164,x10162,x10161))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10165),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10166),a8))
% 1.10/1.34 [1021]E(x10214,x10213)+E(x10211,x10212)+E(x10213,x10212)+E(x10214,x10211)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10214),x10213)),f27(a1,x10216)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10212),x10211)),f27(a1,x10215)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10212),x10211)),f27(x10215,f89(x10215,x10216,x10211,x10212,x10213,x10214))))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10214),x10213)),f27(x10216,f89(x10215,x10216,x10211,x10212,x10213,x10214))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10215),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10216),a8))
% 1.10/1.34 [1022]E(x10224,x10223)+E(x10221,x10222)+E(x10223,x10221)+E(x10224,x10222)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10224),x10223)),f27(a1,x10226)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10221),x10222)),f27(a1,x10225)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10221),x10222)),f27(x10225,f90(x10225,x10226,x10222,x10221,x10223,x10224))))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10224),x10223)),f27(x10226,f90(x10225,x10226,x10222,x10221,x10223,x10224))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10225),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10226),a8))
% 1.10/1.34 [1023]E(x10234,x10233)+E(x10231,x10232)+E(x10233,x10231)+E(x10234,x10232)+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10234),x10233)),f27(a1,x10236)))+P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10231),x10232)),f27(a1,x10235)))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10231),x10232)),f27(x10235,f90(x10236,x10235,x10233,x10234,x10232,x10231))))+~P36(f27(f27(f34(f98(a92,a92)),f27(f27(f32(a92,a92),x10234),x10233)),f27(x10236,f90(x10236,x10235,x10233,x10234,x10232,x10231))))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10235),a8))+~P36(f27(f27(f34(f96(a91,f96(f98(a92,a92),a2))),x10236),a8))
% 1.10/1.34 %EqnAxiom
% 1.10/1.34 [1]E(x11,x11)
% 1.10/1.34 [2]E(x22,x21)+~E(x21,x22)
% 1.10/1.34 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.10/1.34 [4]~E(x41,x42)+E(f3(x41),f3(x42))
% 1.10/1.34 [5]~E(x51,x52)+E(f20(x51),f20(x52))
% 1.10/1.34 [6]~E(x61,x62)+E(f27(x61,x63),f27(x62,x63))
% 1.10/1.34 [7]~E(x71,x72)+E(f27(x73,x71),f27(x73,x72))
% 1.10/1.34 [8]~E(x81,x82)+E(f26(x81,x83),f26(x82,x83))
% 1.10/1.34 [9]~E(x91,x92)+E(f26(x93,x91),f26(x93,x92))
% 1.10/1.34 [10]~E(x101,x102)+E(f9(x101,x103,x104,x105),f9(x102,x103,x104,x105))
% 1.10/1.34 [11]~E(x111,x112)+E(f9(x113,x111,x114,x115),f9(x113,x112,x114,x115))
% 1.10/1.34 [12]~E(x121,x122)+E(f9(x123,x124,x121,x125),f9(x123,x124,x122,x125))
% 1.10/1.34 [13]~E(x131,x132)+E(f9(x133,x134,x135,x131),f9(x133,x134,x135,x132))
% 1.10/1.34 [14]~E(x141,x142)+E(f29(x141),f29(x142))
% 1.10/1.34 [15]~E(x151,x152)+E(f4(x151),f4(x152))
% 1.10/1.34 [16]~E(x161,x162)+E(f16(x161,x163,x164,x165,x166),f16(x162,x163,x164,x165,x166))
% 1.10/1.34 [17]~E(x171,x172)+E(f16(x173,x171,x174,x175,x176),f16(x173,x172,x174,x175,x176))
% 1.10/1.34 [18]~E(x181,x182)+E(f16(x183,x184,x181,x185,x186),f16(x183,x184,x182,x185,x186))
% 1.10/1.34 [19]~E(x191,x192)+E(f16(x193,x194,x195,x191,x196),f16(x193,x194,x195,x192,x196))
% 1.10/1.34 [20]~E(x201,x202)+E(f16(x203,x204,x205,x206,x201),f16(x203,x204,x205,x206,x202))
% 1.10/1.34 [21]~E(x211,x212)+E(f34(x211),f34(x212))
% 1.10/1.34 [22]~E(x221,x222)+E(f60(x221,x223,x224,x225),f60(x222,x223,x224,x225))
% 1.10/1.34 [23]~E(x231,x232)+E(f60(x233,x231,x234,x235),f60(x233,x232,x234,x235))
% 1.10/1.34 [24]~E(x241,x242)+E(f60(x243,x244,x241,x245),f60(x243,x244,x242,x245))
% 1.10/1.34 [25]~E(x251,x252)+E(f60(x253,x254,x255,x251),f60(x253,x254,x255,x252))
% 1.10/1.34 [26]~E(x261,x262)+E(f5(x261),f5(x262))
% 1.10/1.34 [27]~E(x271,x272)+E(f96(x271,x273),f96(x272,x273))
% 1.10/1.34 [28]~E(x281,x282)+E(f96(x283,x281),f96(x283,x282))
% 1.10/1.34 [29]~E(x291,x292)+E(f19(x291),f19(x292))
% 1.10/1.34 [30]~E(x301,x302)+E(f6(x301,x303,x304),f6(x302,x303,x304))
% 1.10/1.34 [31]~E(x311,x312)+E(f6(x313,x311,x314),f6(x313,x312,x314))
% 1.10/1.34 [32]~E(x321,x322)+E(f6(x323,x324,x321),f6(x323,x324,x322))
% 1.10/1.34 [33]~E(x331,x332)+E(f98(x331,x333),f98(x332,x333))
% 1.10/1.34 [34]~E(x341,x342)+E(f98(x343,x341),f98(x343,x342))
% 1.10/1.34 [35]~E(x351,x352)+E(f23(x351),f23(x352))
% 1.10/1.34 [36]~E(x361,x362)+E(f74(x361,x363,x364,x365),f74(x362,x363,x364,x365))
% 1.10/1.34 [37]~E(x371,x372)+E(f74(x373,x371,x374,x375),f74(x373,x372,x374,x375))
% 1.10/1.34 [38]~E(x381,x382)+E(f74(x383,x384,x381,x385),f74(x383,x384,x382,x385))
% 1.10/1.34 [39]~E(x391,x392)+E(f74(x393,x394,x395,x391),f74(x393,x394,x395,x392))
% 1.10/1.34 [40]~E(x401,x402)+E(f28(x401,x403),f28(x402,x403))
% 1.10/1.34 [41]~E(x411,x412)+E(f28(x413,x411),f28(x413,x412))
% 1.10/1.34 [42]~E(x421,x422)+E(f66(x421,x423),f66(x422,x423))
% 1.10/1.34 [43]~E(x431,x432)+E(f66(x433,x431),f66(x433,x432))
% 1.10/1.34 [44]~E(x441,x442)+E(f32(x441,x443),f32(x442,x443))
% 1.10/1.34 [45]~E(x451,x452)+E(f32(x453,x451),f32(x453,x452))
% 1.10/1.34 [46]~E(x461,x462)+E(f97(x461,x463),f97(x462,x463))
% 1.10/1.34 [47]~E(x471,x472)+E(f97(x473,x471),f97(x473,x472))
% 1.10/1.34 [48]~E(x481,x482)+E(f30(x481),f30(x482))
% 1.10/1.34 [49]~E(x491,x492)+E(f69(x491,x493,x494,x495),f69(x492,x493,x494,x495))
% 1.10/1.34 [50]~E(x501,x502)+E(f69(x503,x501,x504,x505),f69(x503,x502,x504,x505))
% 1.10/1.34 [51]~E(x511,x512)+E(f69(x513,x514,x511,x515),f69(x513,x514,x512,x515))
% 1.10/1.34 [52]~E(x521,x522)+E(f69(x523,x524,x525,x521),f69(x523,x524,x525,x522))
% 1.10/1.34 [53]~E(x531,x532)+E(f17(x531,x533,x534,x535),f17(x532,x533,x534,x535))
% 1.10/1.34 [54]~E(x541,x542)+E(f17(x543,x541,x544,x545),f17(x543,x542,x544,x545))
% 1.10/1.34 [55]~E(x551,x552)+E(f17(x553,x554,x551,x555),f17(x553,x554,x552,x555))
% 1.10/1.34 [56]~E(x561,x562)+E(f17(x563,x564,x565,x561),f17(x563,x564,x565,x562))
% 1.10/1.34 [57]~E(x571,x572)+E(f22(x571,x573,x574,x575),f22(x572,x573,x574,x575))
% 1.10/1.34 [58]~E(x581,x582)+E(f22(x583,x581,x584,x585),f22(x583,x582,x584,x585))
% 1.10/1.34 [59]~E(x591,x592)+E(f22(x593,x594,x591,x595),f22(x593,x594,x592,x595))
% 1.10/1.34 [60]~E(x601,x602)+E(f22(x603,x604,x605,x601),f22(x603,x604,x605,x602))
% 1.10/1.34 [61]~E(x611,x612)+E(f35(x611,x613,x614),f35(x612,x613,x614))
% 1.10/1.34 [62]~E(x621,x622)+E(f35(x623,x621,x624),f35(x623,x622,x624))
% 1.10/1.34 [63]~E(x631,x632)+E(f35(x633,x634,x631),f35(x633,x634,x632))
% 1.10/1.34 [64]~E(x641,x642)+E(f36(x641,x643,x644,x645),f36(x642,x643,x644,x645))
% 1.10/1.34 [65]~E(x651,x652)+E(f36(x653,x651,x654,x655),f36(x653,x652,x654,x655))
% 1.10/1.34 [66]~E(x661,x662)+E(f36(x663,x664,x661,x665),f36(x663,x664,x662,x665))
% 1.10/1.34 [67]~E(x671,x672)+E(f36(x673,x674,x675,x671),f36(x673,x674,x675,x672))
% 1.10/1.34 [68]~E(x681,x682)+E(f54(x681),f54(x682))
% 1.10/1.34 [69]~E(x691,x692)+E(f14(x691,x693),f14(x692,x693))
% 1.10/1.34 [70]~E(x701,x702)+E(f14(x703,x701),f14(x703,x702))
% 1.10/1.34 [71]~E(x711,x712)+E(f57(x711,x713),f57(x712,x713))
% 1.10/1.34 [72]~E(x721,x722)+E(f57(x723,x721),f57(x723,x722))
% 1.10/1.34 [73]~E(x731,x732)+E(f37(x731,x733,x734,x735),f37(x732,x733,x734,x735))
% 1.10/1.34 [74]~E(x741,x742)+E(f37(x743,x741,x744,x745),f37(x743,x742,x744,x745))
% 1.10/1.34 [75]~E(x751,x752)+E(f37(x753,x754,x751,x755),f37(x753,x754,x752,x755))
% 1.10/1.34 [76]~E(x761,x762)+E(f37(x763,x764,x765,x761),f37(x763,x764,x765,x762))
% 1.10/1.34 [77]~E(x771,x772)+E(f88(x771,x773,x774,x775,x776),f88(x772,x773,x774,x775,x776))
% 1.10/1.34 [78]~E(x781,x782)+E(f88(x783,x781,x784,x785,x786),f88(x783,x782,x784,x785,x786))
% 1.10/1.34 [79]~E(x791,x792)+E(f88(x793,x794,x791,x795,x796),f88(x793,x794,x792,x795,x796))
% 1.10/1.34 [80]~E(x801,x802)+E(f88(x803,x804,x805,x801,x806),f88(x803,x804,x805,x802,x806))
% 1.10/1.34 [81]~E(x811,x812)+E(f88(x813,x814,x815,x816,x811),f88(x813,x814,x815,x816,x812))
% 1.10/1.34 [82]~E(x821,x822)+E(f79(x821,x823,x824,x825,x826),f79(x822,x823,x824,x825,x826))
% 1.10/1.34 [83]~E(x831,x832)+E(f79(x833,x831,x834,x835,x836),f79(x833,x832,x834,x835,x836))
% 1.10/1.34 [84]~E(x841,x842)+E(f79(x843,x844,x841,x845,x846),f79(x843,x844,x842,x845,x846))
% 1.10/1.34 [85]~E(x851,x852)+E(f79(x853,x854,x855,x851,x856),f79(x853,x854,x855,x852,x856))
% 1.10/1.34 [86]~E(x861,x862)+E(f79(x863,x864,x865,x866,x861),f79(x863,x864,x865,x866,x862))
% 1.10/1.34 [87]~E(x871,x872)+E(f13(x871,x873,x874),f13(x872,x873,x874))
% 1.10/1.34 [88]~E(x881,x882)+E(f13(x883,x881,x884),f13(x883,x882,x884))
% 1.10/1.34 [89]~E(x891,x892)+E(f13(x893,x894,x891),f13(x893,x894,x892))
% 1.10/1.34 [90]~E(x901,x902)+E(f15(x901,x903),f15(x902,x903))
% 1.10/1.34 [91]~E(x911,x912)+E(f15(x913,x911),f15(x913,x912))
% 1.10/1.34 [92]~E(x921,x922)+E(f78(x921,x923),f78(x922,x923))
% 1.10/1.34 [93]~E(x931,x932)+E(f78(x933,x931),f78(x933,x932))
% 1.10/1.34 [94]~E(x941,x942)+E(f31(x941,x943,x944),f31(x942,x943,x944))
% 1.10/1.34 [95]~E(x951,x952)+E(f31(x953,x951,x954),f31(x953,x952,x954))
% 1.10/1.34 [96]~E(x961,x962)+E(f31(x963,x964,x961),f31(x963,x964,x962))
% 1.10/1.34 [97]~E(x971,x972)+E(f41(x971),f41(x972))
% 1.10/1.34 [98]~E(x981,x982)+E(f70(x981,x983,x984,x985,x986),f70(x982,x983,x984,x985,x986))
% 1.10/1.34 [99]~E(x991,x992)+E(f70(x993,x991,x994,x995,x996),f70(x993,x992,x994,x995,x996))
% 1.10/1.34 [100]~E(x1001,x1002)+E(f70(x1003,x1004,x1001,x1005,x1006),f70(x1003,x1004,x1002,x1005,x1006))
% 1.10/1.34 [101]~E(x1011,x1012)+E(f70(x1013,x1014,x1015,x1011,x1016),f70(x1013,x1014,x1015,x1012,x1016))
% 1.10/1.34 [102]~E(x1021,x1022)+E(f70(x1023,x1024,x1025,x1026,x1021),f70(x1023,x1024,x1025,x1026,x1022))
% 1.10/1.34 [103]~E(x1031,x1032)+E(f89(x1031,x1033,x1034,x1035,x1036,x1037),f89(x1032,x1033,x1034,x1035,x1036,x1037))
% 1.10/1.34 [104]~E(x1041,x1042)+E(f89(x1043,x1041,x1044,x1045,x1046,x1047),f89(x1043,x1042,x1044,x1045,x1046,x1047))
% 1.10/1.34 [105]~E(x1051,x1052)+E(f89(x1053,x1054,x1051,x1055,x1056,x1057),f89(x1053,x1054,x1052,x1055,x1056,x1057))
% 1.10/1.34 [106]~E(x1061,x1062)+E(f89(x1063,x1064,x1065,x1061,x1066,x1067),f89(x1063,x1064,x1065,x1062,x1066,x1067))
% 1.10/1.34 [107]~E(x1071,x1072)+E(f89(x1073,x1074,x1075,x1076,x1071,x1077),f89(x1073,x1074,x1075,x1076,x1072,x1077))
% 1.10/1.34 [108]~E(x1081,x1082)+E(f89(x1083,x1084,x1085,x1086,x1087,x1081),f89(x1083,x1084,x1085,x1086,x1087,x1082))
% 1.10/1.34 [109]~E(x1091,x1092)+E(f95(x1091),f95(x1092))
% 1.10/1.34 [110]~E(x1101,x1102)+E(f50(x1101),f50(x1102))
% 1.10/1.34 [111]~E(x1111,x1112)+E(f73(x1111,x1113),f73(x1112,x1113))
% 1.10/1.34 [112]~E(x1121,x1122)+E(f73(x1123,x1121),f73(x1123,x1122))
% 1.10/1.34 [113]~E(x1131,x1132)+E(f86(x1131,x1133,x1134,x1135,x1136),f86(x1132,x1133,x1134,x1135,x1136))
% 1.10/1.34 [114]~E(x1141,x1142)+E(f86(x1143,x1141,x1144,x1145,x1146),f86(x1143,x1142,x1144,x1145,x1146))
% 1.10/1.34 [115]~E(x1151,x1152)+E(f86(x1153,x1154,x1151,x1155,x1156),f86(x1153,x1154,x1152,x1155,x1156))
% 1.10/1.34 [116]~E(x1161,x1162)+E(f86(x1163,x1164,x1165,x1161,x1166),f86(x1163,x1164,x1165,x1162,x1166))
% 1.10/1.34 [117]~E(x1171,x1172)+E(f86(x1173,x1174,x1175,x1176,x1171),f86(x1173,x1174,x1175,x1176,x1172))
% 1.10/1.34 [118]~E(x1181,x1182)+E(f87(x1181,x1183,x1184,x1185,x1186,x1187),f87(x1182,x1183,x1184,x1185,x1186,x1187))
% 1.10/1.34 [119]~E(x1191,x1192)+E(f87(x1193,x1191,x1194,x1195,x1196,x1197),f87(x1193,x1192,x1194,x1195,x1196,x1197))
% 1.10/1.34 [120]~E(x1201,x1202)+E(f87(x1203,x1204,x1201,x1205,x1206,x1207),f87(x1203,x1204,x1202,x1205,x1206,x1207))
% 1.10/1.34 [121]~E(x1211,x1212)+E(f87(x1213,x1214,x1215,x1211,x1216,x1217),f87(x1213,x1214,x1215,x1212,x1216,x1217))
% 1.10/1.34 [122]~E(x1221,x1222)+E(f87(x1223,x1224,x1225,x1226,x1221,x1227),f87(x1223,x1224,x1225,x1226,x1222,x1227))
% 1.10/1.34 [123]~E(x1231,x1232)+E(f87(x1233,x1234,x1235,x1236,x1237,x1231),f87(x1233,x1234,x1235,x1236,x1237,x1232))
% 1.10/1.34 [124]~E(x1241,x1242)+E(f59(x1241,x1243),f59(x1242,x1243))
% 1.10/1.34 [125]~E(x1251,x1252)+E(f59(x1253,x1251),f59(x1253,x1252))
% 1.10/1.34 [126]~E(x1261,x1262)+E(f18(x1261,x1263,x1264,x1265,x1266,x1267),f18(x1262,x1263,x1264,x1265,x1266,x1267))
% 1.10/1.34 [127]~E(x1271,x1272)+E(f18(x1273,x1271,x1274,x1275,x1276,x1277),f18(x1273,x1272,x1274,x1275,x1276,x1277))
% 1.10/1.34 [128]~E(x1281,x1282)+E(f18(x1283,x1284,x1281,x1285,x1286,x1287),f18(x1283,x1284,x1282,x1285,x1286,x1287))
% 1.10/1.34 [129]~E(x1291,x1292)+E(f18(x1293,x1294,x1295,x1291,x1296,x1297),f18(x1293,x1294,x1295,x1292,x1296,x1297))
% 1.10/1.34 [130]~E(x1301,x1302)+E(f18(x1303,x1304,x1305,x1306,x1301,x1307),f18(x1303,x1304,x1305,x1306,x1302,x1307))
% 1.10/1.34 [131]~E(x1311,x1312)+E(f18(x1313,x1314,x1315,x1316,x1317,x1311),f18(x1313,x1314,x1315,x1316,x1317,x1312))
% 1.10/1.34 [132]~E(x1321,x1322)+E(f44(x1321,x1323,x1324),f44(x1322,x1323,x1324))
% 1.10/1.34 [133]~E(x1331,x1332)+E(f44(x1333,x1331,x1334),f44(x1333,x1332,x1334))
% 1.10/1.34 [134]~E(x1341,x1342)+E(f44(x1343,x1344,x1341),f44(x1343,x1344,x1342))
% 1.10/1.34 [135]~E(x1351,x1352)+E(f25(x1351,x1353,x1354,x1355),f25(x1352,x1353,x1354,x1355))
% 1.10/1.34 [136]~E(x1361,x1362)+E(f25(x1363,x1361,x1364,x1365),f25(x1363,x1362,x1364,x1365))
% 1.10/1.34 [137]~E(x1371,x1372)+E(f25(x1373,x1374,x1371,x1375),f25(x1373,x1374,x1372,x1375))
% 1.10/1.34 [138]~E(x1381,x1382)+E(f25(x1383,x1384,x1385,x1381),f25(x1383,x1384,x1385,x1382))
% 1.10/1.34 [139]~E(x1391,x1392)+E(f83(x1391,x1393),f83(x1392,x1393))
% 1.10/1.34 [140]~E(x1401,x1402)+E(f83(x1403,x1401),f83(x1403,x1402))
% 1.10/1.34 [141]~E(x1411,x1412)+E(f90(x1411,x1413,x1414,x1415,x1416,x1417),f90(x1412,x1413,x1414,x1415,x1416,x1417))
% 1.10/1.34 [142]~E(x1421,x1422)+E(f90(x1423,x1421,x1424,x1425,x1426,x1427),f90(x1423,x1422,x1424,x1425,x1426,x1427))
% 1.10/1.34 [143]~E(x1431,x1432)+E(f90(x1433,x1434,x1431,x1435,x1436,x1437),f90(x1433,x1434,x1432,x1435,x1436,x1437))
% 1.10/1.34 [144]~E(x1441,x1442)+E(f90(x1443,x1444,x1445,x1441,x1446,x1447),f90(x1443,x1444,x1445,x1442,x1446,x1447))
% 1.10/1.34 [145]~E(x1451,x1452)+E(f90(x1453,x1454,x1455,x1456,x1451,x1457),f90(x1453,x1454,x1455,x1456,x1452,x1457))
% 1.10/1.34 [146]~E(x1461,x1462)+E(f90(x1463,x1464,x1465,x1466,x1467,x1461),f90(x1463,x1464,x1465,x1466,x1467,x1462))
% 1.10/1.34 [147]~E(x1471,x1472)+E(f51(x1471),f51(x1472))
% 1.10/1.34 [148]~E(x1481,x1482)+E(f85(x1481,x1483,x1484,x1485),f85(x1482,x1483,x1484,x1485))
% 1.10/1.34 [149]~E(x1491,x1492)+E(f85(x1493,x1491,x1494,x1495),f85(x1493,x1492,x1494,x1495))
% 1.10/1.34 [150]~E(x1501,x1502)+E(f85(x1503,x1504,x1501,x1505),f85(x1503,x1504,x1502,x1505))
% 1.10/1.34 [151]~E(x1511,x1512)+E(f85(x1513,x1514,x1515,x1511),f85(x1513,x1514,x1515,x1512))
% 1.10/1.34 [152]~E(x1521,x1522)+E(f42(x1521,x1523,x1524,x1525),f42(x1522,x1523,x1524,x1525))
% 1.10/1.34 [153]~E(x1531,x1532)+E(f42(x1533,x1531,x1534,x1535),f42(x1533,x1532,x1534,x1535))
% 1.10/1.34 [154]~E(x1541,x1542)+E(f42(x1543,x1544,x1541,x1545),f42(x1543,x1544,x1542,x1545))
% 1.10/1.34 [155]~E(x1551,x1552)+E(f42(x1553,x1554,x1555,x1551),f42(x1553,x1554,x1555,x1552))
% 1.10/1.34 [156]~E(x1561,x1562)+E(f43(x1561,x1563),f43(x1562,x1563))
% 1.10/1.34 [157]~E(x1571,x1572)+E(f43(x1573,x1571),f43(x1573,x1572))
% 1.10/1.34 [158]~E(x1581,x1582)+E(f62(x1581,x1583),f62(x1582,x1583))
% 1.10/1.34 [159]~E(x1591,x1592)+E(f62(x1593,x1591),f62(x1593,x1592))
% 1.10/1.34 [160]~E(x1601,x1602)+E(f24(x1601),f24(x1602))
% 1.10/1.34 [161]~E(x1611,x1612)+E(f61(x1611,x1613,x1614,x1615),f61(x1612,x1613,x1614,x1615))
% 1.10/1.34 [162]~E(x1621,x1622)+E(f61(x1623,x1621,x1624,x1625),f61(x1623,x1622,x1624,x1625))
% 1.10/1.34 [163]~E(x1631,x1632)+E(f61(x1633,x1634,x1631,x1635),f61(x1633,x1634,x1632,x1635))
% 1.10/1.34 [164]~E(x1641,x1642)+E(f61(x1643,x1644,x1645,x1641),f61(x1643,x1644,x1645,x1642))
% 1.10/1.34 [165]~E(x1651,x1652)+E(f67(x1651),f67(x1652))
% 1.10/1.34 [166]~E(x1661,x1662)+E(f48(x1661,x1663),f48(x1662,x1663))
% 1.10/1.34 [167]~E(x1671,x1672)+E(f48(x1673,x1671),f48(x1673,x1672))
% 1.10/1.34 [168]~E(x1681,x1682)+E(f52(x1681),f52(x1682))
% 1.10/1.34 [169]~E(x1691,x1692)+E(f71(x1691,x1693),f71(x1692,x1693))
% 1.10/1.34 [170]~E(x1701,x1702)+E(f71(x1703,x1701),f71(x1703,x1702))
% 1.10/1.34 [171]~E(x1711,x1712)+E(f82(x1711,x1713,x1714,x1715),f82(x1712,x1713,x1714,x1715))
% 1.10/1.34 [172]~E(x1721,x1722)+E(f82(x1723,x1721,x1724,x1725),f82(x1723,x1722,x1724,x1725))
% 1.10/1.34 [173]~E(x1731,x1732)+E(f82(x1733,x1734,x1731,x1735),f82(x1733,x1734,x1732,x1735))
% 1.10/1.34 [174]~E(x1741,x1742)+E(f82(x1743,x1744,x1745,x1741),f82(x1743,x1744,x1745,x1742))
% 1.10/1.34 [175]~E(x1751,x1752)+E(f58(x1751,x1753),f58(x1752,x1753))
% 1.10/1.34 [176]~E(x1761,x1762)+E(f58(x1763,x1761),f58(x1763,x1762))
% 1.10/1.34 [177]~E(x1771,x1772)+E(f76(x1771,x1773,x1774,x1775),f76(x1772,x1773,x1774,x1775))
% 1.10/1.34 [178]~E(x1781,x1782)+E(f76(x1783,x1781,x1784,x1785),f76(x1783,x1782,x1784,x1785))
% 1.10/1.34 [179]~E(x1791,x1792)+E(f76(x1793,x1794,x1791,x1795),f76(x1793,x1794,x1792,x1795))
% 1.10/1.34 [180]~E(x1801,x1802)+E(f76(x1803,x1804,x1805,x1801),f76(x1803,x1804,x1805,x1802))
% 1.10/1.34 [181]~E(x1811,x1812)+E(f63(x1811,x1813,x1814,x1815),f63(x1812,x1813,x1814,x1815))
% 1.10/1.34 [182]~E(x1821,x1822)+E(f63(x1823,x1821,x1824,x1825),f63(x1823,x1822,x1824,x1825))
% 1.10/1.34 [183]~E(x1831,x1832)+E(f63(x1833,x1834,x1831,x1835),f63(x1833,x1834,x1832,x1835))
% 1.10/1.34 [184]~E(x1841,x1842)+E(f63(x1843,x1844,x1845,x1841),f63(x1843,x1844,x1845,x1842))
% 1.10/1.34 [185]~E(x1851,x1852)+E(f80(x1851,x1853),f80(x1852,x1853))
% 1.10/1.34 [186]~E(x1861,x1862)+E(f80(x1863,x1861),f80(x1863,x1862))
% 1.10/1.34 [187]~E(x1871,x1872)+E(f72(x1871,x1873),f72(x1872,x1873))
% 1.10/1.34 [188]~E(x1881,x1882)+E(f72(x1883,x1881),f72(x1883,x1882))
% 1.10/1.34 [189]~E(x1891,x1892)+E(f53(x1891),f53(x1892))
% 1.10/1.34 [190]~E(x1901,x1902)+E(f75(x1901,x1903,x1904),f75(x1902,x1903,x1904))
% 1.10/1.34 [191]~E(x1911,x1912)+E(f75(x1913,x1911,x1914),f75(x1913,x1912,x1914))
% 1.10/1.34 [192]~E(x1921,x1922)+E(f75(x1923,x1924,x1921),f75(x1923,x1924,x1922))
% 1.10/1.34 [193]~E(x1931,x1932)+E(f55(x1931,x1933,x1934,x1935),f55(x1932,x1933,x1934,x1935))
% 1.10/1.34 [194]~E(x1941,x1942)+E(f55(x1943,x1941,x1944,x1945),f55(x1943,x1942,x1944,x1945))
% 1.10/1.34 [195]~E(x1951,x1952)+E(f55(x1953,x1954,x1951,x1955),f55(x1953,x1954,x1952,x1955))
% 1.10/1.34 [196]~E(x1961,x1962)+E(f55(x1963,x1964,x1965,x1961),f55(x1963,x1964,x1965,x1962))
% 1.10/1.34 [197]~E(x1971,x1972)+E(f33(x1971,x1973,x1974,x1975),f33(x1972,x1973,x1974,x1975))
% 1.10/1.34 [198]~E(x1981,x1982)+E(f33(x1983,x1981,x1984,x1985),f33(x1983,x1982,x1984,x1985))
% 1.10/1.34 [199]~E(x1991,x1992)+E(f33(x1993,x1994,x1991,x1995),f33(x1993,x1994,x1992,x1995))
% 1.10/1.34 [200]~E(x2001,x2002)+E(f33(x2003,x2004,x2005,x2001),f33(x2003,x2004,x2005,x2002))
% 1.10/1.34 [201]~E(x2011,x2012)+E(f68(x2011,x2013,x2014,x2015,x2016),f68(x2012,x2013,x2014,x2015,x2016))
% 1.10/1.34 [202]~E(x2021,x2022)+E(f68(x2023,x2021,x2024,x2025,x2026),f68(x2023,x2022,x2024,x2025,x2026))
% 1.10/1.34 [203]~E(x2031,x2032)+E(f68(x2033,x2034,x2031,x2035,x2036),f68(x2033,x2034,x2032,x2035,x2036))
% 1.10/1.34 [204]~E(x2041,x2042)+E(f68(x2043,x2044,x2045,x2041,x2046),f68(x2043,x2044,x2045,x2042,x2046))
% 1.10/1.34 [205]~E(x2051,x2052)+E(f68(x2053,x2054,x2055,x2056,x2051),f68(x2053,x2054,x2055,x2056,x2052))
% 1.10/1.34 [206]~E(x2061,x2062)+E(f56(x2061),f56(x2062))
% 1.10/1.34 [207]~E(x2071,x2072)+E(f49(x2071),f49(x2072))
% 1.10/1.34 [208]~E(x2081,x2082)+E(f84(x2081),f84(x2082))
% 1.10/1.34 [209]~E(x2091,x2092)+E(f40(x2091,x2093),f40(x2092,x2093))
% 1.10/1.34 [210]~E(x2101,x2102)+E(f40(x2103,x2101),f40(x2103,x2102))
% 1.10/1.34 [211]~E(x2111,x2112)+E(f77(x2111,x2113,x2114,x2115,x2116),f77(x2112,x2113,x2114,x2115,x2116))
% 1.10/1.34 [212]~E(x2121,x2122)+E(f77(x2123,x2121,x2124,x2125,x2126),f77(x2123,x2122,x2124,x2125,x2126))
% 1.10/1.34 [213]~E(x2131,x2132)+E(f77(x2133,x2134,x2131,x2135,x2136),f77(x2133,x2134,x2132,x2135,x2136))
% 1.10/1.34 [214]~E(x2141,x2142)+E(f77(x2143,x2144,x2145,x2141,x2146),f77(x2143,x2144,x2145,x2142,x2146))
% 1.10/1.34 [215]~E(x2151,x2152)+E(f77(x2153,x2154,x2155,x2156,x2151),f77(x2153,x2154,x2155,x2156,x2152))
% 1.10/1.34 [216]~E(x2161,x2162)+E(f81(x2161),f81(x2162))
% 1.10/1.34 [217]~P1(x2171)+P1(x2172)+~E(x2171,x2172)
% 1.10/1.34 [218]~P2(x2181)+P2(x2182)+~E(x2181,x2182)
% 1.10/1.34 [219]~P4(x2191)+P4(x2192)+~E(x2191,x2192)
% 1.10/1.34 [220]~P5(x2201)+P5(x2202)+~E(x2201,x2202)
% 1.10/1.34 [221]~P36(x2211)+P36(x2212)+~E(x2211,x2212)
% 1.10/1.34 [222]~P6(x2221)+P6(x2222)+~E(x2221,x2222)
% 1.10/1.34 [223]~P28(x2231)+P28(x2232)+~E(x2231,x2232)
% 1.10/1.34 [224]P13(x2242,x2243)+~E(x2241,x2242)+~P13(x2241,x2243)
% 1.10/1.34 [225]P13(x2253,x2252)+~E(x2251,x2252)+~P13(x2253,x2251)
% 1.10/1.34 [226]~P29(x2261)+P29(x2262)+~E(x2261,x2262)
% 1.10/1.34 [227]P14(x2272,x2273,x2274,x2275)+~E(x2271,x2272)+~P14(x2271,x2273,x2274,x2275)
% 1.10/1.34 [228]P14(x2283,x2282,x2284,x2285)+~E(x2281,x2282)+~P14(x2283,x2281,x2284,x2285)
% 1.10/1.34 [229]P14(x2293,x2294,x2292,x2295)+~E(x2291,x2292)+~P14(x2293,x2294,x2291,x2295)
% 1.10/1.34 [230]P14(x2303,x2304,x2305,x2302)+~E(x2301,x2302)+~P14(x2303,x2304,x2305,x2301)
% 1.10/1.34 [231]~P30(x2311)+P30(x2312)+~E(x2311,x2312)
% 1.10/1.34 [232]~P7(x2321)+P7(x2322)+~E(x2321,x2322)
% 1.10/1.34 [233]~P8(x2331)+P8(x2332)+~E(x2331,x2332)
% 1.10/1.34 [234]~P9(x2341)+P9(x2342)+~E(x2341,x2342)
% 1.10/1.34 [235]~P10(x2351)+P10(x2352)+~E(x2351,x2352)
% 1.10/1.34 [236]~P11(x2361)+P11(x2362)+~E(x2361,x2362)
% 1.10/1.34 [237]~P20(x2371)+P20(x2372)+~E(x2371,x2372)
% 1.10/1.34 [238]~P24(x2381)+P24(x2382)+~E(x2381,x2382)
% 1.10/1.34 [239]~P12(x2391)+P12(x2392)+~E(x2391,x2392)
% 1.10/1.34 [240]~P23(x2401)+P23(x2402)+~E(x2401,x2402)
% 1.10/1.34 [241]~P25(x2411)+P25(x2412)+~E(x2411,x2412)
% 1.10/1.34 [242]~P21(x2421)+P21(x2422)+~E(x2421,x2422)
% 1.10/1.34 [243]~P22(x2431)+P22(x2432)+~E(x2431,x2432)
% 1.10/1.34 [244]~P33(x2441)+P33(x2442)+~E(x2441,x2442)
% 1.10/1.34 [245]~P26(x2451)+P26(x2452)+~E(x2451,x2452)
% 1.10/1.34 [246]~P31(x2461)+P31(x2462)+~E(x2461,x2462)
% 1.10/1.34 [247]~P35(x2471)+P35(x2472)+~E(x2471,x2472)
% 1.10/1.34 [248]~P27(x2481)+P27(x2482)+~E(x2481,x2482)
% 1.10/1.34 [249]P19(x2492,x2493,x2494,x2495)+~E(x2491,x2492)+~P19(x2491,x2493,x2494,x2495)
% 1.10/1.34 [250]P19(x2503,x2502,x2504,x2505)+~E(x2501,x2502)+~P19(x2503,x2501,x2504,x2505)
% 1.10/1.34 [251]P19(x2513,x2514,x2512,x2515)+~E(x2511,x2512)+~P19(x2513,x2514,x2511,x2515)
% 1.10/1.34 [252]P19(x2523,x2524,x2525,x2522)+~E(x2521,x2522)+~P19(x2523,x2524,x2525,x2521)
% 1.10/1.34 [253]P3(x2532,x2533)+~E(x2531,x2532)+~P3(x2531,x2533)
% 1.10/1.34 [254]P3(x2543,x2542)+~E(x2541,x2542)+~P3(x2543,x2541)
% 1.10/1.34 [255]P18(x2552,x2553)+~E(x2551,x2552)+~P18(x2551,x2553)
% 1.10/1.34 [256]P18(x2563,x2562)+~E(x2561,x2562)+~P18(x2563,x2561)
% 1.10/1.34 [257]P15(x2572,x2573,x2574,x2575,x2576)+~E(x2571,x2572)+~P15(x2571,x2573,x2574,x2575,x2576)
% 1.10/1.34 [258]P15(x2583,x2582,x2584,x2585,x2586)+~E(x2581,x2582)+~P15(x2583,x2581,x2584,x2585,x2586)
% 1.10/1.34 [259]P15(x2593,x2594,x2592,x2595,x2596)+~E(x2591,x2592)+~P15(x2593,x2594,x2591,x2595,x2596)
% 1.10/1.34 [260]P15(x2603,x2604,x2605,x2602,x2606)+~E(x2601,x2602)+~P15(x2603,x2604,x2605,x2601,x2606)
% 1.10/1.34 [261]P15(x2613,x2614,x2615,x2616,x2612)+~E(x2611,x2612)+~P15(x2613,x2614,x2615,x2616,x2611)
% 1.10/1.34 [262]P16(x2622,x2623,x2624,x2625,x2626,x2627)+~E(x2621,x2622)+~P16(x2621,x2623,x2624,x2625,x2626,x2627)
% 1.10/1.34 [263]P16(x2633,x2632,x2634,x2635,x2636,x2637)+~E(x2631,x2632)+~P16(x2633,x2631,x2634,x2635,x2636,x2637)
% 1.10/1.34 [264]P16(x2643,x2644,x2642,x2645,x2646,x2647)+~E(x2641,x2642)+~P16(x2643,x2644,x2641,x2645,x2646,x2647)
% 1.10/1.34 [265]P16(x2653,x2654,x2655,x2652,x2656,x2657)+~E(x2651,x2652)+~P16(x2653,x2654,x2655,x2651,x2656,x2657)
% 1.10/1.34 [266]P16(x2663,x2664,x2665,x2666,x2662,x2667)+~E(x2661,x2662)+~P16(x2663,x2664,x2665,x2666,x2661,x2667)
% 1.10/1.34 [267]P16(x2673,x2674,x2675,x2676,x2677,x2672)+~E(x2671,x2672)+~P16(x2673,x2674,x2675,x2676,x2677,x2671)
% 1.10/1.34 [268]~P32(x2681)+P32(x2682)+~E(x2681,x2682)
% 1.10/1.34 [269]P17(x2692,x2693,x2694,x2695,x2696,x2697)+~E(x2691,x2692)+~P17(x2691,x2693,x2694,x2695,x2696,x2697)
% 1.10/1.34 [270]P17(x2703,x2702,x2704,x2705,x2706,x2707)+~E(x2701,x2702)+~P17(x2703,x2701,x2704,x2705,x2706,x2707)
% 1.10/1.34 [271]P17(x2713,x2714,x2712,x2715,x2716,x2717)+~E(x2711,x2712)+~P17(x2713,x2714,x2711,x2715,x2716,x2717)
% 1.10/1.34 [272]P17(x2723,x2724,x2725,x2722,x2726,x2727)+~E(x2721,x2722)+~P17(x2723,x2724,x2725,x2721,x2726,x2727)
% 1.10/1.34 [273]P17(x2733,x2734,x2735,x2736,x2732,x2737)+~E(x2731,x2732)+~P17(x2733,x2734,x2735,x2736,x2731,x2737)
% 1.10/1.34 [274]P17(x2743,x2744,x2745,x2746,x2747,x2742)+~E(x2741,x2742)+~P17(x2743,x2744,x2745,x2746,x2747,x2741)
% 1.10/1.34 [275]~P34(x2751)+P34(x2752)+~E(x2751,x2752)
% 1.10/1.34
% 1.10/1.34 %-------------------------------------------
% 1.10/1.35 cnf(1037,plain,
% 1.10/1.35 (~P36(f27(f27(f29(a93),f27(f27(f19(a93),x10371),x10372)),x10372))),
% 1.10/1.35 inference(rename_variables,[],[402])).
% 1.10/1.35 cnf(1040,plain,
% 1.10/1.35 (~P36(f27(f27(f29(a93),x10401),x10401))),
% 1.10/1.35 inference(rename_variables,[],[397])).
% 1.10/1.35 cnf(1047,plain,
% 1.10/1.35 (P36(f27(f27(f29(a93),x10471),f27(a21,x10471)))),
% 1.10/1.35 inference(rename_variables,[],[323])).
% 1.10/1.35 cnf(1052,plain,
% 1.10/1.35 (~P36(f27(f27(f29(a93),f27(f27(f19(a93),x10521),x10522)),x10522))),
% 1.10/1.35 inference(rename_variables,[],[402])).
% 1.10/1.35 cnf(1055,plain,
% 1.10/1.35 (~P36(f27(f28(a93,f27(a21,x10551)),x10551))),
% 1.10/1.35 inference(rename_variables,[],[401])).
% 1.10/1.35 cnf(1069,plain,
% 1.10/1.35 (P36(f27(f28(a93,x10691),x10691))),
% 1.10/1.35 inference(rename_variables,[],[315])).
% 1.10/1.35 cnf(1072,plain,
% 1.10/1.35 (P36(f27(f28(a93,x10721),f27(f27(f19(a93),x10722),x10721)))),
% 1.10/1.35 inference(rename_variables,[],[337])).
% 1.10/1.35 cnf(1075,plain,
% 1.10/1.35 (P36(f27(f28(a93,x10751),f27(f27(f19(a93),x10752),x10751)))),
% 1.10/1.35 inference(rename_variables,[],[337])).
% 1.10/1.35 cnf(1080,plain,
% 1.10/1.35 (~P36(f27(f27(f29(a93),f27(f27(f19(a93),x10801),x10802)),x10802))),
% 1.10/1.35 inference(rename_variables,[],[402])).
% 1.10/1.35 cnf(1086,plain,
% 1.10/1.35 (P36(f27(f27(f29(a93),x10861),f27(a21,x10861)))),
% 1.10/1.35 inference(rename_variables,[],[323])).
% 1.10/1.35 cnf(1089,plain,
% 1.10/1.35 (P36(f27(f28(a93,x10891),f27(f27(f19(a93),x10892),x10891)))),
% 1.10/1.35 inference(rename_variables,[],[337])).
% 1.10/1.35 cnf(1094,plain,
% 1.10/1.35 (~P36(f27(f28(a93,f27(a21,x10941)),x10941))),
% 1.10/1.35 inference(rename_variables,[],[401])).
% 1.10/1.35 cnf(1097,plain,
% 1.10/1.35 (~P36(f27(f28(a93,f27(a21,x10971)),x10971))),
% 1.10/1.35 inference(rename_variables,[],[401])).
% 1.10/1.35 cnf(1105,plain,
% 1.10/1.35 (P36(f27(f28(a93,x11051),x11051))),
% 1.10/1.35 inference(rename_variables,[],[315])).
% 1.10/1.35 cnf(1146,plain,
% 1.10/1.35 (~P36(f27(f27(f29(a93),x11461),x11461))),
% 1.10/1.35 inference(rename_variables,[],[397])).
% 1.10/1.35 cnf(1149,plain,
% 1.10/1.35 (P36(f27(f27(f29(a93),x11491),f27(a21,x11491)))),
% 1.10/1.35 inference(rename_variables,[],[323])).
% 1.10/1.35 cnf(1155,plain,
% 1.10/1.35 (P36(f27(f28(f96(x11551,a2),x11552),f35(x11551,x11553,x11552)))),
% 1.10/1.35 inference(rename_variables,[],[350])).
% 1.10/1.35 cnf(1158,plain,
% 1.10/1.35 (P36(f27(f28(f96(x11581,a2),x11582),f35(x11581,x11583,x11582)))),
% 1.10/1.35 inference(rename_variables,[],[350])).
% 1.10/1.35 cnf(1171,plain,
% 1.10/1.35 (P36(f27(f27(f34(x11711),x11712),f30(f96(x11711,a2))))),
% 1.10/1.35 inference(rename_variables,[],[331])).
% 1.10/1.35 cnf(1176,plain,
% 1.10/1.35 (P36(f27(f28(f96(x11761,a2),x11762),x11762))),
% 1.10/1.35 inference(rename_variables,[],[328])).
% 1.10/1.35 cnf(1182,plain,
% 1.10/1.35 (E(f36(x11821,x11821,f5(x11821),x11822),x11822)),
% 1.10/1.35 inference(rename_variables,[],[336])).
% 1.10/1.35 cnf(1187,plain,
% 1.10/1.35 (P36(f27(f28(f96(x11871,a2),x11872),x11872))),
% 1.10/1.35 inference(rename_variables,[],[328])).
% 1.10/1.35 cnf(1202,plain,
% 1.10/1.35 (E(f26(a93,x12021),x12021)),
% 1.10/1.35 inference(rename_variables,[],[304])).
% 1.10/1.35 cnf(1206,plain,
% 1.10/1.35 (~E(f27(a21,x12061),x12061)),
% 1.10/1.35 inference(rename_variables,[],[389])).
% 1.10/1.35 cnf(1238,plain,
% 1.10/1.35 (~P36(f27(f27(f29(a93),x12381),x12381))),
% 1.10/1.35 inference(rename_variables,[],[397])).
% 1.10/1.35 cnf(1249,plain,
% 1.10/1.35 ($false),
% 1.10/1.35 inference(scs_inference,[],[279,281,282,289,290,294,385,387,342,311,303,358,346,345,344,405,367,354,379,335,304,1202,389,1206,321,395,336,1182,315,1069,1105,328,1176,1187,397,1040,1146,1238,401,1055,1094,1097,350,1155,1158,323,1047,1086,1149,400,313,314,331,1171,340,337,1072,1075,1089,402,1037,1052,1080,373,355,2,410,489,476,467,861,860,516,487,473,454,418,573,482,796,765,763,751,750,681,672,670,652,651,650,648,646,641,640,624,622,597,592,577,553,550,548,526,490,488,598,519,840,543,466,907,900,895,864,852,846,818,806,727,688,926,809,795,888,871,887,854,843,892,944,958,889,980,259,255,230,228,227,225,221,219,3,456,515,514,469,446,444,865,787,605,497,496,695,862,606,684,637,586,572]),
% 1.10/1.35 ['proof']).
% 1.10/1.35 % SZS output end Proof
% 1.10/1.35 % Total time :0.280000s
%------------------------------------------------------------------------------